Installing double-pole line-voltage thermostat
Take your thermostat back and get a refund

Your existing setup relied on the way double pole 240V thermostats work -- one leg is an ON/OFF (disconnect) function, while the other leg is thermostatically controlled.  This is fine for running electric resistance heaters, and also in the case of a mechanical thermostat abusable for what the original installer did to control the fans ON/OFF and pump thermostatically.

However, an electronic thermostat like yours needs power for its own functions.  While I'm not clear on how you wired it to get it to turn on at all, it certainly won't work correctly with both of its incoming hots on the same leg, in any case.

How to do things the right way

To actually control your system with a programmable thermostat, you'll need four things (and possibly a fifth if the installer was a cheapskate):


A double relay module that mounts to a 1/2" KO and can handle the fan + pump loads (a RIBT242B with a 4" box cover works)
A 24VAC/40VA Class 2 transformer that mounts to a 1/2" KO (such as the Functional Devices TR40VA040)
A 24VAC (low voltage) programmable thermostat (use your favorite -- you have your pick here)
Some 18/2 CL2 thermostat wire
Optionally, a 4" square metal box that can be mounted as the old box was (if the old box was plastic, it likely lacks conduit KOs) and matching cover
And basic electrical supplies (electrical tape, wirenuts) as well as the ability to hole and patch the wall


Installation is as follows:


Turn power off at the panel
Remove and replace the box with the 4" square metal box if the existing box does not have 1/2" conduit knockouts
Install the transformer and relay to the box -- the relay's uncovered side needs to face the front and poke through the wall surface, and you'll need some access to the wall cavity to get at the transformer terminals and thread cable about.
Put a hole in where you want the thermostat to go.  Run two pieces of thermostat cable -- one to the transformer terminals, and the other to the relay.  Mark the one that goes to the relay with a tape flag.
Take the cable that goes to the transformer terminals and connect it to the transformer terminals: red to one (this'll be your R wire) and white to the other (this'll be your C wire).  Take a third length of cable and connect it to the transformer terminals the same way, then run it to the relay.
Mark the cable that came from the thermostat location to the relay with a tape flag, then stick both cables through one of the holes in the relay box.  The red and white wires on the flagged cable go to the relay 1 and 2 coil screw terminals, respectively (red in this cable is W, and white is G).  The white wire from the unflagged cable goes to the relay coil common screw terminal, while the red in the unflagged cable is capped with a wirenut.
Wire up the thermostat as follows:


Red from the unflagged cable goes to R or Rh
White from the unflagged cable goes to C
Red from the flagged cable goes to W
White from the flagged cable goes to G

Wire up the wires in the junction box as follows:


The two "always hot" blacks from the wall are wired to each other, to the white wire from the transformer, and to the yellow and purple wires from the relay
The orange and red wires from the transformer and the blue and grey wires from the relay are individually capped off
The white neutral wires from the wall are all wired to each other, and to the black common wire from the transformer
The red wires from the wall that control the fans are wired to the orange wire from the relay
The black wires from the wall that control the pump are wired to the brown wire from the relay
All grounds (bare or green wires) are connected to each other, and to a grounding pigtail to the box if the box is metal

Put covers on the box and the relay
Turn the power back on at the panel.
Patch up any holes in the wall that aren't covered by something or the other.
Program your new thermostat and enjoy!