Learn English – How to change the tense of a hyphenated verb

The term in question is phrasal verb which is defined as

a phrase which consists of a verb in combination with a preposition or adverb or both, the meaning of which is different from the meaning of its separate parts. ^Cambridge

When changing the tense of a phrasal verb, only the verb is affected, for the simple reason that adverbs and prepositions do not change with tense, as they are not verbs. It is also crucial to note that phrasal verbs do not come with hyphens. However, a number of them can be hyphenated or compounded to function as adjectives or nouns with related or unrelated meanings.

To use your example, the past tense of mouse over would be moused over, while the present participle would be mousing over. You could also hyphenate to make a noun, as in, "The trackball is so bad that a simple mouse-over to the top-left corner of the screen takes more than twenty seconds."

For reference, here is the definition of mouse over:

mouse (verb)
[with adverbial of direction] use a mouse to move a cursor on a computer screen:
mouse over to the window and click on it ^NOAD

Some standard phrasal verbs, their tenses and their adjective/noun derivatives:

PHRASAL VERB   PAST TENSE      PRESENT PARTICIPLE     ADJECTIVE/NOUN
brush off      brushed off     brushing off           brush-off
fall out       fell out        falling out            fallout • falling-out
check in       checked in      checking in            check-in
cross over     crossed over    crossing over          crossover
drop out       dropped out     dropping out           dropout
knock down     knocked down    knocking down          knockdown • knock-down
see through    saw through     seeing through         see-through      
shape up       shaped up       shaping up             shape-up
stand by       stood by        standing by            standby
take away      took away       taking away            takeaway
take off       took off        taking off             takeoff • take-off

All this said, there are indeed some standard hyphenated verbs (these belong to the larger group of compound verbs, majority of which do not have a hypen, e.g. backstab, broadside, singsong, overtake, bypass, etc.), but these are not verb-preposition combinations, as you indicated. Rather, they terminate in verbs or are wholly verbal in composition. For these species, the tense change affects the word in its entirety. Examples:

COMPOUND VERB     PAST TENSE       PRESENT PARTICIPLE
(with hyphen)
booby-trap        booby-trapped    booby-trapping
flip-flop         flip-flopped     flip-flopping
see-saw           see-sawed        see-sawing
sun-dry           sun-dried        sun-drying
T-bone            T-boned          T-boning

However, there exists one (and there may be a few more) true hyphenated phrasal verb (verb-preposition) that is treated wholly as a verb: one-up

PHRASAL VERB   PAST TENSE      PRESENT PARTICIPLE     ADJECTIVE/NOUN
one-up         one-upped       one-upping             one up [on]

It appears, however, that this verb may be a back-formation from the original noun phrase and, later, adjective, one up.