These things are contextual.

"x increases three times" means 3x to most people. This is different from "increases by 300%" which usually means 4x. The article says "by a factor of up to three" in the first sentence but that is too wordy for a headline.

> what happens if 30 “increases by 1 times”?

Nobody would ever say this. We would say it doubled or stayed the same, or "increased by 100%" perhaps, but never "increased by 1 time".

> 30 “increases by 2 times mean?”

Nobody would ever say this either.

That's why I prefer to say "it increased from 30 to 120" and let the reader calculate if they want to. At least the right info is there. :)

This reminds me of the wording in my son's homework two days ago. So much interpretation involved. I wish they would choose the wording of their questions more closely in those math homeworks (and also in articles).

For reference, his homework question was something along the lines of:

If the auditorium currently has five rows of ten chars in place, and they need three times more chairs, how many more rows of ten chairs do they need?