Rebecca, in past:
1. "Я вчера заходил на кафедру, но тебя там не было."
- Ты был на вчерашней лекции?
- Нет, я там не был.
Both speak of absence.
But in (1) we speak, being focused at the place itself. The place 'lacked' your presence when we observed the place. When we came, we couldn't find you there. And 'impersonal' form is used (literally "it-were not of-you")
In (2) I speak about what I did (and did not) yesterday. I MYSELF am 'lacking' an experience of being present during that lecture. Besides my answer mirrors the form from your question.
If in (1) I say "я заходил на кафедру, но[а] ты там не был" - that will sound not as "I couldn't find".
Rather it sounds "I came there [in 5 p.m.]. But as we both know, you didn't go there yesterday [in any moment]".
It is uncommon wording and needs special context. E.g. you were expected to come earlier and leave somethign for me there. Or it is said to explain why I have some news (e.g. refurbishment) about the place, and you don't know this (in this case 'a' instead of 'но' as there is no contradition).
There are also borderline cases where both form can be used.
Now future. In past we speak of experience (mine or yours) that has already... been experienced:) So mostly when I speak of myself - i refer to MY experience. As for your experience, you already know what it was.
In 1st person (2) is much more common.
We dont' have experiences about future, only expectations. And quite often I can assume "teacher's" point of view and say
"не будет". I will be absent. He won't see me there. He shouldn't expect me there.
When I speak from MY point of view, I'd use "Я туда завтра не пойду".
"не буду" is quite uncommon wording...
Possible as an answer to "ты там будешь?" question, but uncommon otherwise.