Ok, yeah those things get rewired by idiots quite frequently... and you're correct to follow the schematic for wiring the thing, (as long as the previous ahem... 'person' didn't change anything behind it).
The function of the second air button on those things is normally for a light switch, not control functions.
The heater.. yes you are correct, it should not connect electrically to the controller. It's turned on only by water pressure and thermostat setting. The thermostat can be self contained in the gas heater, or remote like on your wall. Just a real cheap speaker/bell wire thing works fine with these as it's usually dependent on pilot generator voltage (like 600 millivolts dc) to turn the gas valve on and off. If it's electronic ignition type of heater, then it'll usually have 24 vac running through it. It's just a simple kill switch with a temp sensor.
The timer, will turn on and off the
pump (low speed) that's connected to the heater and filter. The other pump should not have low speed connected to anything. It should only work as a secondary high speed pump. So while it may sound a little convoluted, the spa can only heat when someone has the jets turned on, or the timer says it's time to filter.. AND the thermostat says the water's too cold.
Now if you energize the high speed thing by pushing the button... it will break the low speed voltage, and switch over to the high speed leg. (You can never have high and low speed applied at the same time to a pump motor!). In any event, if the heater's thermostat has indicated a need for heat to the spa, as long as there's water pressure, it'll kick on and heat up. This controller and heater combination will always be independent of each other. Electric/electronic spa controllers work entirely different from this so prepare yourself... they're actually more fun to work on than these older designs.
Now when you get through with this and look back at how ridiculous this situation was, maybe you can see how I got hooked into this crazy biz so long ago... Every other customer I went to... it was "now what nut case wired this thing!!!", or "unreal, it's a wonder nobody was electrocuted or the house hasn't burned down yet"... ugh!
