First of all, I would never say either
正しく推測していました under any circumstances. They sound very odd.
If I have to use the word 推測, I would use it as a noun.
You can use の to specify whose guess it was, and it can be anyone.
If I have to use 推測 in its verb form, I would still nominalize it with こと.
(正しかった can be replaced with 正しい but let’s leave it aside in this discussion.)
In everyday conversation, it is more common to use a plainer verb like 思う.
These two are different in that the former describes a change of state of mind that happened at one point of time, while the latter refers to a state of mind that lasted for some period. This difference is not that important when you are talking about yourself. However, since you cannot tell when exactly some change occurred to another person’s inner state (unless they express it somehow), the first form is not usually used for anyone other than the speaker.
The same difference applies when a verb is used as the predicate.
Both are good if you are talking about yourself, while only the second is appropriate if you are talking about a third person, except in a novel or a voice-over where the narrator describes the state of mind of a character objectively. One thing you need to be careful with here is that neither sentence is appropriate if you are talking about the second person. This is for a different reason than what we have discussed so far: you don’t tell someone what they thought as if you know better.
It is OK to ask that person using either form.