Is being the second author out of two authors for papers from my PhD thesis going to affect my future job prospects?
There are a lot of variables here. I'm in the US and personally never considered the order of authors significant, assuming generally that all were contributors. But in other places and with other persons it may be different. Do people assume that the first (or last) author is the "real author" and everyone else gets a free ride? I hope that isn't so. But I can't guarantee it. 

Many people, it seems, include their dissertation advisor on papers arising from that work. I doubt that it is necessary and others are recommended to ask the advisor before they send the paper for publication. Many would suggest they not be included, but other advisors would have other advice. You might be able to avoid the OP's dilemma. 

For purposes of job applications it will be useful, of course, if these are not the only papers you have in publication. If you have a few more, on which you are the sole author you will likely be in a good place. 

However, your job prospects depend on more than your CV. Focus on that. If someone is hiring and gets a lot of applications, the first thing they do, typically, is to sort the candidates into two piles. The big pile is people who won't be considered. You want to get yourself into the small pile, but that will depend on more than the publications on your CV, including what you say about yourself in the opening (cover) letter. It will depend on your experience as well and how suitable your background is for the advertised job. 

If you can make up a complete application package that gets you into the small pile, then your concern won't matter at all, since you will probably get an interview for the job and, if necessary, explain that this work was your dissertation work, done by you, with appropriate assistance. Your respect for your advisor led you to list him/her first. I don't think you can successfully explain that other than in person, however. It isn't the sort of thing that should be in the CV. 

However, it might be possible to add a parenthetical note to the listings of the articles that this paper was based on your dissertation. Don't say more, however, and be careful even about that. I suggest it as a possibility, but don't necessarily recommend it.

But, again, your goal is to get an interview in which you can show the interviewers how suitable you are for the position. 

And write a lot of papers as sole author if possible.