To an extent you are right, but it's more about the embarrassment of a man rather than a negative depiction of a woman as having to "be in her place", since two accepted cultural norms are that men should avoid being passengers as we are meant to be the leader in any given situation as well as the fact that it's a man riding a scooter, what is considered by the more masculine oriented grouping of men to be a motorbike for women, meaning that the depiction of that man on his girlfriends scooter is reliant on showing him as both forfeiting his inherent responsibility to lead and control, a somewhat sexist but forgivable goal and forfeiting that right by riding what is considered one of the most emasculating vehicles in existence.
This is based on your description, I possibly get different ads to you (Australian) but from what you're saying the ad is just following that "BE MANLY BY DOING MAN STUFF" method that a lot of ads are moving towards when targeting younger men. It is somewhat old fashioned, but as an ideal men riding as a passenger on a scooter can, in a modern society, still be seen as an emasculating experience, and an acceptable way to highlight the implied masculinity of the product through showing who, according to the product, needs it.
So overall, no matter the context of the ad, most men would recognize being a passenger on a scooter to be embarrassing through it's depiction of power in the relationship (woman in control) so while a little sexist in that way, it's mostly harmless and childish.