I'm a little disappointed. It seems as if it will bloom once, make fruit, then die. Is that correct?
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Not quite so. I don't think so.
Firstly, plant wont die until maybe frost(depending on the climate).
Secondly, there are different kinds of determinants. Some come to fruits in one flush and then quit, some continue all summer. In other words , there are some tomatoes that have DETERMINANT growth habit but fruit like INDETS.

I grew all determinates my first year. Instead of thinking of everything maturing and then the plants dying all at once, just think of a smaller harvesting window than indeterminates have. I had tomatoes coming in for probably a month. If you intend to can your tomatoes this is a good thing; it allows you to harvest a lot at once, and therefore process fewer times.

Last year I have no idea what I grew - they were all leftovers from local high school experiments that the kids had left behind.

This year I have mostly indeterminates under grow lights, but I intend to swap for a few determinates as well.

Determinates will continue to grow and set tomatoes, just at a reduced rate after the first big flush of tomatoes. The determinates in our high tunnels act differently, they act more like indeterminates in that they continue to grow and set. We usually get two big flushes of tomatoes, the second one is less than the first.

We have started growing more and more determinates for our market gardens. They fit our production model better and they meet the needs and wants of our customers. We do 5 to 6 plantings of tomatoes, about 3 to 4 weeks apart. The first planting should have been planted, but it has not been. We will probably have planted at least 5 plantings before we harvest a single tomato. But when they start, we will have a steady supply until Thanksgiving time. We plant fewer plants with each planting as the previous planting will still be producing, just at a reduced rate. In August-October, we will be picking from all the plantings, but the newest one will get the most attention.

Jay

Should I pinch them to promote more growth before it blooms since it will only bloom once?

No. As others have explained it doesn't just bloom once or even all at once. Blooms develop as the plant grows until it reaches its terminal top blooms at 4-6 feet depending on the variety That can take several months. Removing blooms only costs you fruit.

To get the most from the plants you don't remove anything - no blooms, no stems, no branches, etc. :)

Dave

Here is a link that might be useful: FAQ - Determinate vs. Indeterminates

Due to weather last year I had an awful year for tomatoes. The one plant that kept giving off fruit. Even in the dog days of 100 degree plus dog days was a det. plant. It was a husky cherry red. We got well over 150 of the tiny maters from June till October. I had it planted in an area that got good shade after 5 pm.