You have presented the start of a sentence in the form
- When [noun phrase] (,) came home ...
and you're asking whether the comma I've placed in parentheses should be present when the noun phrase is a list that employs the Oxford comma.
No, that comma should be omitted.
The closest that Strunk and White come to this is the discussion on parenthetical expressions (rule 3). Your example isn't one, but the associated commentary is of some interest:
This rule is difficult to apply; it is frequently hard to decide whether a single word, such as however, or a brief phrase, is or is not parenthetic. If the interruption to the flow of the sentence is but slight, the writer may safely omit the commas. But whether the interruption be slight or considerable, he must never omit one comma and leave the other.
There is no considerable interruption between the phrases my sister and came home in your example. It's arguable that there isn't an interruption at all. As such, even if this was a parenthetical expression, "the writer may safely omit the commas".
For a more relevant reference, consider Guide to Using Commas by Penn State Berks Writing Center:
2 Don’t use a comma to separate the subject from the verb.
- Incorrect: An eight-year-old boy, is coming to the party.
- Correct: An eight-year-old boy is coming to the party.
In your example, the noun phrase "my mom, my dad, and my sister" is the subject and "came" is the verb. They shouldn't be separated by a comma. Whether the Oxford comma is used in the noun phrase is irrelevant.
Nevertheless, your question specifically asks about the lists containing the Oxford comma:
Is there a comma after a list with an Oxford comma?
If you consider that list to be a unit, the answer will depend on the place that unit holds within the sentence. Here are some examples:
He came, saw, and conquered (,) Rome. Omit the comma in parentheses because He [verb phrase] [noun] doesn't require a comma between the verb phrase and the noun.
This man, pin-striped, skinny, and mean-looking (,) was lurking behind the gate. Include the comma in parentheses because pin-striped, skinny, and mean-looking is a parenthetical expression, and the trailing comma matches the leading comma (after man and before pin-striped).