I think they refer to early on in perimenopause where you may be experiencing anovular cycles. When this happens an egg is not released so the corpus luteum (which is formed from the follicle it was released from) does not produce progesterone. Or eggs may be released, but they are a bit past it and the corpus luteum not very strong). Oestrogen levels may get high for longer until they drop in the absence of ovulation. They call it oestrogen dominance and this is also a theory put forward by John Lee. However it does not have very widespread agreement.
The ovaries do not seem to give up gracefully and that was certainly the case for me!
It is worth reading The Perils of Perimenopause in the information tabs above.
Every month can be different and oestrogen levels can go up and plummet, resulting in a withdrawal bleed (which is like a period but it is not and as the progesterone has not modified the lining it does not come away well causing more bleeding and leaving some behind). If you replace the progesterone in the second half to complete the cycle, it gets better organised. Usually you can get progestogens like norithisterone, or mirena and have them continuously because the cycle is erratic, and they also stop build up of lining.
I think the oestrogen in hrt helps as it stops your levels reaching rock bottom and gives a bit more stability.
I used to get really bad night sweats on the pill. They got much worse in the last 4 years when I had other menopause like symptoms. The only reason I can find is that progestogen raises your body temperature a little (and there is an awful lot of it in the pill) and that this must have pushed me into the zone where it is hard to regulate temperature during menopause