With all due respect OP, I think he is feeding you a load of bullshit.
He has cottoned on you were getting suspicious of this woman and has changed tact. Please just think about this for a second:
When you gave her a lift with DH in the car she was dismissive of you, spoke only to DH and looked at you while discussing his shifts with him (from the old thread). Did not thank you for the lift, only said goodbye to DH.
This equate to there was very likely something on some level already going on bewteen them.
Your DH has said he has found out she has form for this (coming onto men?)and has done it with another collegue.
This equates to him showing her as a predator so anything you hear from now on is all on her - not his fault, shes a predator.
Your DH has said his manager has had a word with him.
A manager would not have a word with someone if a collegue was just following them around and chatting about them. The manager has had a word because it has become obvious there is something going on between them and it is affecting his and her work. I imagine something along the lines of they are being caught chatting toegther when should be working, a little too often.
Him telling you this will manager conversation took place also cover his arse if you ever found out the manager was suggesting something going on, and also again paints her as the predator, so not his fault, poor lamb.
He however does not yet appear to have done anything about this.
This equates to because he doesn't want to.
He is asking to change his shifts
Have you seen his request? Could it be the manager is actually demanding he change his shifts because neither of them are getting their jobs done because of all the flirting. Or he is changing his shifts because the OW is and he wants to still continue to work with her.
He is going to stop giving lifts
If he really was being propositioned by this peredator and was not interested, he would have already stopped the lifts. When will the lift stopping be happening exactly? Because there should be zero more lifts.
He is being more attentive to you
Of course he is. You are suspicious and you are right. He nees to sort that out doesn't he so you can stop being suspicious and he can go back to whatever it was he was doing without feeling guilty.
To sum up (his version): he is being chased by this woman, his manager has warned him about it, he needs to change his shifts to work with her less, but hes still currently giving her lifts because on top of all that hes too nice to just say to her, sorry no more lifts?
Sorry, it sounds to me like hes covering his tracks and coming out with a ton of bullshit.
In terms of your self esteem, from what you have posted about this man previously, I think the best thing for your self esteem would be to distance yourself from him