past tense vs present tense in apologizing

Living in Japan, I've noticed that when it comes to either apologizing or saying, ''Thanks for your hard work,'' there doesn't seem to be any strict guidelines for present and past tense.

For example, if I've committed a mistake I should say すみません. But would it make a difference if I say すみませんでした instead? Or does that just translate to, ''I was sorry?'' This applies to 垂ｵ訳ございません too.

Or if someone is leaving work (and they worked hard) I often hear お疲れさまです rather than お疲れさまでした. While their work is obviously in the past, why keep it in the present voice? Is it better to use the past tense if one was talking about the work one did yesterday, and tell that person お疲れ様でした?

Again, another example... 分かります versus 分かりました.

Thank you in advance.

you'll typically only hear 'sumimasen' in the present, so just go with the flow and use it that way.

as for otsukaresama deshita and desu, I hear it usually with deshita. As the concept of this phrase is: "it has been tyrying for you" but you can do it either way.

[ 垂ｵ訳ございません / すみません / 失礼します ]

I suppose でした can follow 垂ｵ訳ございません / すみません when an apology has been already accepted and the speaker hopes to mention his/her mistake later.
While the speaker is apologizing, でした usually does not appear in a phrase of the apology itself.

A similar thing can be said about 失礼します [shitsureishi-masu] and 失礼しました .
When a schoolchild enters a teachers' room he/she says 失礼します , and when he/she leaves the room he/she says 失礼しました .
One thing to note is that 失礼します is not commonly used in apologies, while失礼しました (or失礼いたしました to be more polite) can be.

失礼します literally means "will do rude" but is also used in saying goodbye. A newscaster may use it when closing his/her news show.

Maybe you have learned that 垂ｵ訳ございませんです and すみませんです are awkward.
And, 失礼です cannot make an apology; it is used to say that someone is rude.

垂ｵ訳ございません is a formal expression preferred in writing and used only in apologies.
すみません was originally meaning like "I don't think I can get off with this ( = such an apology)" but is now commonly used not only in apologies but often as a conversation starter.
You can use すみません for "Sorry" when you hope to say "Sorry to interrupt you,..." and for "Excuse me" when you hope to say "Excuse me to ask,...."

You say すみません if you made a mistake or call for an attention.
すみませんでした a reply when someone points your short fall, mistake, rudeness, etc. that you knew, didn't notice or don't remember.
垂ｵ訳ございません is when you are formerly apologetic to your superior (boss, customer, etc.).
垂ｵ訳ございませんでした　is when you apologize the past to them.
Casual goodbye, see you later is お疲れさん.
お疲れさま、お疲れさまです is a polite frequent greeting to your Senpai or boss leaving the work place that you are not sure whether the reason is work related or slacking off.
お疲れさまでした is a greeting when someone returns from off site work(meeting, trip, etc.)or when it is late enough that you can safely leave the office without resentment from others or boss. Say "お疲れさまでした" out loud　to get attention of others, if you want to embarrass someone leaving work early you know さぼる.
上のNuance/sensitivityは分かりますか？

分かります is when you are sympathetic.
分かりました is when you understood an instruction or an order.