Here are the growth times I've seen on my the MusicStar:baby + 1 hour = toddler
toddler + 24 hours = teen
teen + 30 hours = adult
adult + 3 days = mates offered (twice a day, for four days)
adult + 7 days = oldie
oldie + 3 days = mates offered again (not sure how many times)
Note: The above are unpaused times.
The Band Manager (working as a match-maker) arrived with a prospective mate twice a day (at 12:30 PM & 4:30 PM) for 4 days, at ages 5, 6, 7, 8.
If you have a band member of the gender opposite to your character's, they may visit at 8:00PM, at age 7, proposing marriage.
Downloading your MusicStar may restart the old-enough-to-get-married-after-turning-adult timer. If your adult was too young to be married when you downloaded, you may have to wait 3 days after the download to be able to get married.