In the meantime, have you tried parazone toilet wipes for the floor?
Alice does it by accident sometimes and it either goes on the floor which is wood thankfully or 1/2 in, 1/2 out. If I see her in the tray ready to drop, I say "In a bit" and she always obliges
Anyway, I pick up the worst with a tissue then wipe the floor/edge of tray with the toilet wipes - it takes no time and they can be flushed
As for dealing with the habit, if you keep putting the poo in the tray, hopefully Jet will get the message.
PS - the wipes are 1/2 price in Sainbury's right now
(I have about 20 packs
)