[V た-form]-ら puts focus on a point on the timeline, real or hypothetical, where some action or even has just completed. You focus this point because something happens then.
You might perform another action.
These are examples of the second verb denoting an intentional act by the same person as the first.
You might notice something.
The second verb is used in the past tense but it doesn’t denote an intentional act. This is also true when you say 部屋の窓が開いていることに気づいた as 気づく is not something you intentionally do.
Your action might cause another person to react in some way.
Your examples are both unnatural. You open your mouth to say something. You don’t start saying something upon completion of opening of the mouth. When I hear 口を開いたら, I would expect to hear something like this.
In all these cases, たら marks some change in the course of action or event. It works as a switch, so to speak.
Now, when you are talking about two consecutive actions actually performed in the past by the same person, such a switch is uncalled for and たら would sound completely out of place.
There are other ways to connect the two actions in logically more natural flows.
You can still use たら if the second action is something you would or could have done but didn’t.
In other words, if you use an action verb in the past tense like that, it would be interpreted as an unreal event.
Some dialects, such as Kansai-ben, use たら more liberally than the standard variant of Japanese. As a speaker of one such dialect, I find 口を開いたら失礼なことを言う (without つい) to be totally acceptable as a sentence about someone who habitually says rude things, but 口を開けば would be considered more correct, at least more formal, in standard Japanese. 口を開く is used in a figurative sense here. たら is usually used for a concrete instance.
I try to answer the questions asked in the comments below, though it's hard to answer "why".
When you say 宝くじに当たったら家を買う, you are putting yourself at the point (on a hypothetical timeline) at which you've just won a lottery and stating what you're going to do from that point. Hence the past tense for the first verb and the non-past for the second.
When you talk about a sequence of actions you (or anyone else) knowingly performed in the past from the vantage point of the present, you should have no reason to put yourself at or particularly focus such a point in the middle.
たら is followed by a verb in the past tense when the completion of the first action triggered some reaction or resulted in some discovery. It puts focus on the point at which you felt the impact of such an event. A second intentional action by the same person doesn't require or deserve such a focus.