Undershirt tzitzit were introduced onto the tallit katan market about two decades ago. But I suspect there were similar designs many years ago. If you open up the Chayei Adam to Hilchot Tzitzit 11, 9, the Chayeh Adam [Rabbi Avraham Danzig, 1748-1820], describing various tallit katan designs and whether they would require tzitzit, writes, “And therefore one must be careful with the tallit katan made in our country [probably referring to Saxony and Prussia] that the sides be mostly open; not like those tailors who make a tallit katan and sew it along the sides and leave a hole for the arms and then sew beneath the hole and leave it open, and measure only beneath the arms, which is clearly a mistake, because then [the garment] is not considered to have four kanfos, and we can say with near certainty that one who receites [the Tzitzit Blessing] recites a blessing in vain.”
Indeed, this problem does come up. I know of one importer who made a batch of about 30,000, all of which were definitely more closed than open along the sides.
Note that Mishkan Hatchelet’s patented design on their undershirt (“Cotton Comfort“) eradicates this problem entirely, because the sides are almost entirely open, with just a narrow band fairly high up holding them together.
What about the hechsher? Take a close look, and you’ll see that the hechsher is on the tzitzit strings and the tzitzit tying, not the tallit katan garment. One rav I spoke recently with expressed surprise that a rav would supervise tzitzit tying on a garment that does not require tzitzit. But that fact is that even with traditional cotton tallit katans, you won’t find a hechsher on the beged.
Another issue is the tzitzit holes. They should be positioned 5 cm from the sides of the tallit katan. If the hole is 4.5 cm or 5.5 cm, that’s fine, but if it’s under 4 cm or over 7 we start to run into questions.
Some poskim are against the whole idea of undershirt tzitzits, saying the tallit garment must be a bone fide garment, not an undershirt whose task is to absorb sweat. In my opinion, even according to that opinion, a tzitzit t-shirt would be fine, because it is clearly designed to serve as a genuine garment, not just as an undershirt.
What about undershirt tzitzit for boys? Does it have to be more open than closed along the sides? I really don’t know, you’ll have to ask a qualified rabbi. On one hand, the mitzvah here is chinuch, not the actual mitzvah of tzitzit, and in any case the garment probably does not meet the minimum size requirement, but on the other hand he is probably reciting a bracha on the tzitzit, which can be problematic — especially if he is beyond bar mitzvah age.