Learn English – From when to when/what time to what time

In this context, the term when points out a specific point in time (when you left the apparment), while the phrase by the time… suggests a passage of time that took too long.

So your 2nd sentence (when I left…) better conveys what you are trying to say. The first sentence (by the time I left…) doesn't really convey the correct circumstances of your assertion.

For example:

The injuries didn't look too serious, but by the time the ambulance arrived, the victim was dead.
(Specifies that the delay was at issue)

versus:

The injuries didn't look too serious, but when the ambulance arrived, the victim was dead.
(Still technically correct, but missing the passage of time as an issue)

Sometimes that context is important, so the two phrases are not always interchangeable.

When you turn on the switch, the light goes on. — correct

By the time you turn on the switch, the light goes on. — doesn't make sense

Person 2 is being dreadfully picky in my opinion. For one, to say that something "sounds very ghetto" as a negative is pretty insulting to anyone who lives in a ghetto. There are certain racial and social undercurrents to this statement that are far too complex to go into here as well. To get an idea for yourself, google "ghetto speech" and you will see a wide range of interesting material, as well as a good deal of hateful and racist commentary.

Suffice it to say that "where is it at?" as opposed to "where is it?" is somewhat "slangy" but also commonly used, at least in American English. Whether or not it is technically grammatically incorrect, it is common enough that most people just don't care.

Also, the informal idiom where it's at generally means a fashionable place where the most interesting things are happening at present. By extension, it can be used to refer to people, things or activities as well:

Studio 54 is where it's at.
Whole wheat spaghetti is where it's at.
Kant's Critique of Pure Reason is where it's at.

And so on.