Why is 灸 pronounced jiu1?
This is not an answer but some references that might be helpful and are too long for the comments section.

This is clearly a phenomenon because the first note written on 灸 in《规范》says:

注意 ㊀不读jiū。

But, without much of an explanation it is hard to see why they mention it other than the obvious idea that it often gets mispronounced this way.

As for southern dialects《现代汉语方言音库 • 成都话音档》has the following entry:

灸
tɕiəu⁵⁵

The tone is noted as:

⁵⁵

Which is clearly 阴平, the same as jiu1.

Looking through the tones on: 灸 | Wiktionary we also have:
A high flat tone:

Hakka = /ki̯u⁵⁵/

and a middle flat tone:

Cantonese = /kɐu̯³³/