no you don't need to puncture the grow bag. cut open the bag as indicated on the bag. There are usually instructions on the grow bag too. don't be tempted to add more plants than recommended though.

Are you standing the grow bags on their ends or laying them flat? There's so many different types of grow bag pot...
I wouldn't slit them as the plastic may split further. I use grow bags on their ends with no pots for tomatoes & I always puncture the bottoms in a dozen places with a Phillips screwdriver.
The type of toms you're growing makes a difference. They're either 'determinate' bush types or 'indeterminate' vine types so you need to know which you've got.
Once the weather warms up you'll probably need to water containers twice daily, once as early as possible in the morning & once about sunset perhaps. They like feeding, a high nitrogen fertiliser fortnightly until the first flowers appear then switching to something like Tomorite until fruit appear.
With vine type toms you'll need to pinch out side shoots &, as they get large remove leaves to ensure good air circulation & pinch out the tops once flowers/fruit appear to limit upward growth.
Goodness! Too many things☺

Sorry SeaG, have to disagree, you do need to add drainage holes / slits to base of growbag or it wll just becomes stagnant mess

Depending on make it may have where to puncture marked on base. Some makes are pre punnctured

I've grown them several times without drainage holes & they were OK.Guess it depends on where you are growing them and how warm and dry it gets.

If you don't add drainage holes, you just have to be carefull not to overwater them, but tomatoes are very thirsty plants. Sounds like a lot of work to be honest.

Trouble is you'll only know how warm & dry it gets in retrospect.
Stitch in time & all that...

well the ones we have had in the past have had lots of perforations in them and never had any go stagnant but they were in the greenhouse. perhaps we have just been luck. in recent years we have used the compost from the bags but grown the plants in 3 litre pots with drainage holes. the pots then sunk into the ground. they have a drip irrigation on a timer so any excess water drains into the soil of the greenhouse.

I have to say that I have little faith in growbags. My tomatoes are grown in the soil inside my greenhouse which makes them easier to support. You do need to refresh the soil after a few years. I would always go for growing in pots rather than bags as the watering is less critical. If you have already bought the bags, perhaps do as SBG suggests and use the compost in pots instead.

Mine go straight into the ground, in a bed prepared with lots of manure & compost so the roots can go unrestricted. I can see the benefits of a greenhouse in many respects.