That is not true of any insulin. Hypoglycemia is the first side effect manufacturer's list in their package inserts. The ideal basal insulin onset time would be zero minutes, with no peak, no tail, and produce no hypos. And it would work the same way every time, in every body, every day. There is currently no basal insulin that can be perfect like that.
Tresiba, however, comes a lot closer to that ideal than any other basal insulin. It's not fussy about what time of day you take it. It doesn't even seem to care with consistent time of day dosing, just that doses be separated by at least 8 hours every day. The manufacturer noted that overnight hypos did go down in studies it made. They did not eliminate night-time hypos or at other times of day.
Benefits are alway relative, not absolute. Tresiba appears to work better, in the opinion of many, than competing basal insulins. You will always have to conduct your own personal experiments, pay attention, adjust, and try again. Diabetes is just not a fix it and forget disease. Its nature is dynamic and you will need to move with it if you hope to master its demands. It may be more complicated than you anticipate but it is a solvable puzzle.
To answer your question, I take two pen-shots for each meal and often take 3-4 corrections each day comprised of pen-shots, intra-muscular injections, and Afrezza. I think Tresiba is well worth your time to experiment with. I also highly you encourage to get a stand-alone Dexcom CGM. It is worth it's weight in gold. It will allow you to educate yourself how your body deals with insulin, food, exercise, and a host of other factors that effect blood glucose.
I also think that pump therapy is well worth the effort but your situation, just starting out with very low doses, I would prefer multiple daily injections. But that's me; you need to start giving these options a try so you can make up your own mind.
Good luck! This will not look so complicated 6-12 months from now.