Tub pump pump is running but water is not circulating.

most hot tubs have two motors. one is a circulation pump to move water when the heater starts and the other comes on when the jets are being used. from the sounds of it, the one pump isnt running properly

Depending on the design tubs and pools need water to be circulating before heater runs to prevent the heater from burning out. If the circulation pump runs constantly the heater should work any time but a plugged or restricted filter might not let it flow like it needs to.
If the pump only runs in the jet mode then it might be the way it is designed.
Try checking with the manufacturers website for an FAQ section.

controls operate the pump to circulate the water..there are controls for bubbles and an air pump to increase the volume of the bubbles..and a setting to run the tub slower to allow heating of the water..

Water heater can be added to any incoming water line, either on hot or cold.
http://waterheatertimer.org/How-to-install-under-counter-water-heater.html
Under-counter water heater located near tub will supply hot water just like ordinary household water heater. But it will not reheat water that circulates inside the spa tub.
Otherwise, a spa heater is made with electric element that can work with 120V or 240V. Water from tub circulates through tank that holds element. Element must be fully immersed in water.
To retrofit spa tub with this heater would require cutting water line near pump, running both ends of water line into tank with element.
Then of course you would need to retrofit adjustable thermostat to control when element is on. And integrate element operation into air control switch at tub that can override thermostat so element is not heating when tub is not in use.
Unless there is a pre-packaged kit to retrofit heater, I think adding heater would be difficult.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Check your suction plumbing to be sure it is sealed and tight. Then force some water through the pipe to see if anything is blocking it.

It sounds like your circulation pump is not keeping up with the heater. Check for debris in the pump impeller. If this is 24 hour circulation pump, it is probably failing. New units are about $200 US

you may have a system that uses a small circulating pump that circulates the water thru the heater to keep water temp at proper level (this is usually the case with hot springs spas and is because it is the most cost effective way to maintain constant water heat without using a full size pump or two speed pump just to push water past the heater core. therefore the issue is you have a problem with your jet pump and it has nothing to do with the circulating and heating portion of the spa. you can check to see if there are any reset buttons in or near the equipment as well as open enclosures to make sure everything is clean and dry also make use any contacts on spa skirting are secured propertly

Sounds as if the 'mode' for the tub is set to sense the temperature of the water. see if there is a setting on the control box to a 'timed' setting for filtering and heating instead of controlled by the temperature setting. the problem is the the control box is away from the water and when it calls for heat it is because the water is cooler there than in the hot tub. so when it calls for heat and the water starts to circulate it gets the hot water from the body of the hot tub and then shut down because it senses the 'hot water'. make sense?

You must keep your circulator pump running if you want the water to stay hot. The water is being heated inside the pipes but it isn't getting circulated until you turn on the jets pump.