Should a constant vacuum be out in grow room?

I’m setting up the exhaust system.

Do I want a fan to pull air constantly to create a vacuum or will it kicking on every 3 minutes create negative pressure in the grow room?

Yes you want a constant, even if gentle, pull of air through the grow room to actually maintain negative pressure. Unless you are supplementing with CO2, and negative pressure wouldn’t work very well with that type of setup. The plant will transpire, pulling CO2 out of the air, and putting moisture and O2 into the room’s air, the lights will add heat to the room, by having a gentle turnover of fresh air from outside the grow room, you introduce dryer lower temperature air that will have slightly higher levels of CO2. Most grow rooms won’t be air tight enough to benefit from having a pump periodically turn on and most inline fans will not hold any sort of pressure or lack of pressure when turned off. Depending on what you are trying to do, what kind of fan or fans you have, you could very well have enough air turned over to accomplish control of temperature and humidity, even with only periodic turn over.

So an exhaust fan kicking on every 3- 4 minutes and with another fan running all the time for constant vacuum would keep room full of CO2?

Yes. There is plenty of CO2 in plain old air for most peoples grows. If you have one fan removing air from the room constantly, yes it should provide mildly lower pressure inside the room, or a weak vacuum inside the room. It depends of course if the fan’s cubic feet or meter per hour rating is sufficient for your space. I don’t think it is plausible to have very very large spaces constantly operated at a low pressure. Keeping the pressure low in the room only really serves one purpose, to contain the smell. If you have a fan moving enough air out of the room then any leaks will be pulling fresh air in and not allowing the smell to drift out, and then all the stinky air you are pulling out of the room is sent through a carbon filter to scrub the smell and or treated to an ionizing air freshener as well in some cases, so none of the outgoing air smells. If you just want fresh air for the CO2, then you don’t need to be running negative pressure inside the room all the time.

I was going to have one-two exhaust fans.One to keep a constant vacuum the other to be able to empty room in 3-4 minutes or can you run one inline fan through filter 24/7?It might be simplier to use one big inline fan.
Two or more revolving fans inside the room one below the canopy the other on top

You really should get a thermostat/humidistat, instead of guessing how long to run the exhaust system. This will allow you to set the temps, and humidity limits; which will activate you exhaust system when necessary.

I got a unit on ebay years ago for 80 bucks, and still use it to activate my vortex fan carbon scrubber unit.