When DO is used in an ordinary declarative (positive) sentence it expresses emphatic assertion, usually in contrast to a prior negative. In speech it receives primary stress.
Jill is too shy to work well on teams, but she does work well on her own.
Speaker A: Jack doesn't work here any more.
Speaker B: He does work here, but he's on the night shift.
In older English the DO forms were employed more freely, alternating with simple present and past. You will find it frequently in Shakespeare:
O she doth teach the torches to burn bright!
Why, man, they did make love to this employment.
But it had largely disappeared from the Standard dialect by the 18th century, and survives today only in dialects.
- It is raining.
- It was raining.
- She has gone.
- She had gone.
- They are influenced.
- They were influenced.
- They can leave.
- They could leave.
Another term for "helping verbs" is "auxiliary verbs".
In each sentence in (1-8) we can see an auxiliary verb and a main verb. In English only the first auxiliary can have any tense. In the sentences above we can see that in (1,3,5,7) the auxiliaries are in the present tense. In sentences (2,4,6,8) they are in the past tense.
The verbs after the auxiliaries never have any tense. In English we have three verb forms that have no tense. There are two participles: the -ing form and the 3rd form. There is also the plain form.
We use the -ing form in continuous constructions such as (1,2). Notice that only the auxiliary changes when we go from present tense to past tense. We can use a past or present tense auxiliary with the same participle, raining.
We use the 3rd form in perfect constructions such as the present perfect or past perfect as shown in sentences (2, 3). Again notice that only the auxiliary verb changes when we go from present tense to past tense. We can use a past or present tense auxiliary with the same participle gone. Notice that for many irregular verbs the 3rd form is different from the past tense form. The past tense of GO is went not gone.
We also use the 3rd form in passive constructions as shown in sentences (4, 5). Again notice that the only the auxiliary changes when we go from present tense to past tense. We can use a past or present tense auxiliary with the same participle, influenced. Notice that even though the past tense form of many verbs looks the same as the 3rd form, we only see the third form after auxiliary verbs. Here we see the 3rd form of INFLUENCE, not the past tense!
In sentences (7,8) we see past and present forms of the modal auxiliary verb CAN. Notice that we always use a plain form after modal verbs. It doesn't matter what tense the modal verb is in.
Conclusion
When we have auxiliary verbs or 'helper verbs', only the first auxiliary verb in the verb phrase has tense. All the verbs afterwards are always participles or plain forms. Participles and plain forms have no tense. In English the 3rd form and the past form often look the same. But the verbs we see after an auxiliary are never past tense. Therefore, both of the Original Poster's sentences are perfectly grammatical.
Grammar notes:
Some grammars and EFL course books call the -ing form the 'present participle' and the 3rd form the past participle. These are stupid names for these words. These words have no tense. We can use the past participle in present tense sentences and the present participle in past tense sentences. The grammarians who gave these words these stupid names died a long time ago, so we don't need to be angry with them any more.
According to some grammars, modal verbs don't have tenses. However, most grammarians agree that they do.
Best Answer
SHORT ANSWER:
The simple present and simple past are by definition verb constructions which are not accompanied by auxiliaries (helping verbs). That's why they're called "simple".
LONGER ANSWER:
First, a terminological note: When I speak of "tense" below I don't mean the many single- and multi-word verb chains which English teachers and students often call tenses. I call these "constructions". By "tense" I mean the past or non-past time reference expressed by inflection: a change in the form of the verb, such as adding an ending or changing the pronunciation.
Do, does and did are used in present- and past-tense affirmative sentences; in fact, the principal use of this construction is to emphasize that a response is affirmative:
However, do/does/did are not used with finite forms of the main verb: forms which express and are inflected for tense, person and number. No auxiliary is ever used with a finite form, only with non-finite forms which have no tense, person or number.
The auxiliaries have and be are used with participles of the main verb:
Note that with most English verbs—'regular' verbs—the past participle (broken, here) and the past-tense finite form are identical, which leads many learners to think that the auxiliaries are used with the past-tense form. But so many English verbs—'irregular' verbs—have different past-tense and past participle forms, and those verbs are used so frequently, that we have to make the distinction them in order to make sense of how the language works. —Hold on to that thought; we're going to come back to it shortly.
All other auxiliaries (do/does/did and the 'modal' auxiliaries can, could, may, might, must, shall, should, will, would) are used with the infinitive form of the main verb.
This, again, is difficult for learners to recognize, because with every verb except one the infinitive form is identical with the plain present form. ...
Then why do we give a different name to the form we use with do/does/did and the modal auxiliaries? —for two reasons:
Unlike the many English verbs which have distinct past participle and past-tense forms, there is only one verb which does have a distinct infinitive form. But that verb is be, which is so central to the language that it can't be treated as a minor exception. Note that we never use any of the present- or past-tense forms with the modal auxiliaries or with the 'infinitive marker' to:
Consequently, we distinguish the infinitive from the identical plain present-tense form for the same reason we distinguish the regular past participle from the identical regular past-tense form: because it lets us make sense of how these constructions are built.
Historically, the infinitive and the present form were different, marked with different endings. Those endings were lost in the course of the transition from Old English to Modern English, but there are still 'traces' of the difference in English syntax. Once more the distinction of identical forms enables us to recognize important rules of the language.
For instance, there is the rule that in any verb construction only the first verb in the chain can be a finite form; all the rest must be non-finite forms.
That's what's happening with I do listen and He does like your cookies and I did get a haircut: the first verb, a finite form of DO, is inflected for tense, person and number, and it is followed by the infinitive form of the main verb, listen, like, get.