I’ve got a 38 Ocean (Playtime) so can only guess at your layout. However, it sounds similar with 2 tanks, a pump and accumulator (the ’empty’ upside down bottle) and a Y valve. The Y valve on Playtime switches between the 2 tanks i.e. the system takes it feed from one or the other tank, depending on the lever position, but not both simultaneously. On ours, with the handle in due north (vertical) position, water is drawn from the front tank and with the handle pointing east it connects to the rear tank. Yours may well be oriented differently but you get the picture.
When you get this problem are both tanks full? One possibility is that it is connected to an almost empty tank and that accounts for the spurts.
As you suggest, the accumulator should fill to about two thirds under pressure from the pump when all taps are off. Is the pump still running when you turn off all taps or does it fill the accumulator (to two thirds) and then switch off? If the former, then it is not getting enough water (maybe an empty tank?); if the latter, then the problem lies elsewhere (in which case I’ll need to think a bit more!).
Hope that helps (and I’m not stating the b – – – – – – g obvious).