I'm not familiar with that toy, so I can't really answer if a budgie would be able to successfully press the buttons with the beak or not.
Possibly a budgie could inadvertently press the buttons while standing on the toy and that would be due to the body weight while perching/sitting on it.
Personally, I wouldn't use such toy for my budgies or lovebirds (or any other bird, really).
Just the fact that it has a mirror on it is a big no-no. For lovebirds, they could easily detach the buttons and the toy could turn into an hazard.
If the budgies happen to chew on the toy, with time significant damage can also be done and the risks for the budgies would also be similar.
RIP sweet Tito (Summer 2008 - January 17th 2013).
You are missed and never will be forgotten.