Yoma 6a - Boel nidah

The gemara describes three time ranges for when she finds the blood, in terms of the tum'ah of boel nidah. The first is אויתיום, immediately - they are tamei vadai. The second is אחר, which Rashi gives as the time כדי שתרד מן המטה ותדיח את פניה של מטה
from the gemara in Nidah 14a - they are tamei בספק. After that (אחר אחר) the man is only tamei according to Rabbi Akiva, and only as a gezeirah.

The Ritva says explicitly that the first two are מה"ת, in the first case (immediate) he brings a חטאת, and in the second case (אחר) he brings an אשם תלוי.

I find it all hard to understand. We are presumably referring to a case when she is not בשעת ווסתה: as the gemara says, we are not dealing with רשעים. So there is no chazaka that she will see, and presumably we know she was tehorah before. So we contrast that with the fact that she is known to be a niddah later, and I guess the earlier chazakah wins; we say tahorah till the latest possible time (except for a gezeirah אליבא דר"ע).
But what is this middle case? Where does that time come from; how does it change the situation into a ספק מה"ת? Is it based on some kind of סברא described by the name (כדי שתרד etc.) or is that just a way for Chazal to identify a certain time period?

I guess I should go learn Nidah, but can someone help explain this?

I haven't seen much on this, but maybe this is a way to approach it. "כדי שתרד מן המטה ותדיח" - enough time for her to wash. That is, women wash themselves frequently, and don't leave blood there for very long. Once there has been enough time for her to wash, we can assume that any blood that has been there for a while is gone. Whatever we find is from recently.

Thus, after the time "אחר", if we find blood, we can assume that it followed the ביאה. Does that mean that she didn't see blood before? No - but we have no evidence, and we have a חזקה מעיקרא that tells us to assume that she was tehorah until we have evidence.

Within the time period "אחר", if we see blood, there is no basis for assuming that it necessarily happened after the ביאה; even if it was before the ביאה, there wasn't time for it to go away. We end up with a real ספק.