I understand that it is confusing situation, but at the other hand, it is a good welcome to the world of self-developing. The 'right' development time depends on a lot of things, for instance what the next step of the process will be. Are you intend to make wet prints in a darkroom for instance, or are you going to scan them? And when wet printing: are you using a condensor enlarger or one with a colour head? Other things that may influence the development time is the accuracy of your thermometer for instance. At the other hand: the process is pretty forgiving and films have a quite some lattitude to compensate for errors.
The most important thing when developing your films is to be consistent and to evaluate carefully: do everything the same every time and when changing something: only one factor at the time so you get clue how it affects the process. When evaluating film development you look at two or three things. Firstly there are the highlights: is there enough detail in them? In landscape photography this typically means that you look at the sky and see if there are shades of grey in it. Blown out highlights typically indicate to much development, to much grey indicates underdevelopment. An old trick is to put a negative on some printed text, which should be about just readable through the darker parts of the negative. When printing in a darkroom you should be able to get a decent print on grade 2.5, while perhaps helping the sky with a bit of burning.
The second thing to look after is shadow detail. Putting a negative on a light box or holding them against a bright light will tell you if there is. When not: the negatives need more exposure. A third thing to evaluate is overall scale of tone. That is rather subjective and also depends on what you are going to do after you have developed your prints. Personally I don't like the tonal scale of Pan F very much, even when it is an excelent film and lots of people enjoy using it.
So the advice i would like to give you for a first time film development: when intending to make prints on a condensor enlarger or scan them: slightly softer negatives are generally prevered, so use a time of say 9.30 for the Tri-X and 10 min. or 10.30 min for the TMY. When printing on a colour head: develop half a minute longer and then go from there.