A religious testimony might include the ways in which a speaker attests to the ways their God has worked in their life to sanctify them for His service. As an example, a testimony could include how He brought them through a difficult time in their life (such as a loss of some sort or a severe illness) and built their faith in Him through that experience.
As such, I see nothing wrong with speaking about an addiction overcome, an illness healed, a tragedy averted, etc. For the speaker, I can understand how experiences such as these could bolster their faith and how they would wish to convey this testimony to others of their same faith. If I discover a mathematical theorem, I will naturally want to speak of it to others who have studied mathematics and can more fully appreciate its implications, and not to my friends and family whose eyes will immediately glaze over and begin finding ways to leave the room. It's natural to want to share certain experiences with those who can more deeply relate to them.
However, I think the issue here is about testimony that provides compelling evidence to those who don't share the same faith as the speaker. I doubt that's what Alithis had in mind when he began the other thread. I took that original thread to be a calling from one Christian to others to speak about how they feel God has worked in their lives.
Now, Strav was asking how Alithis' testimony about being delivered from his former addiction to tobacco would work to convince people of other beliefs that this deliverance could only be attributed to the Christian God. The answer here, plain and simple, is that it can't. As has been pointed out, people have been known to quit tobacco cold turkey, by sheer force of will without appealing to the Christian God, or to any supernatural agent.
So, I think if Alithis were to concede this point, and Strav were to concede that Alithis didn't originally intend for his testimony to be regarded by everyone regardless of faith as "compelling evidence" of anything, then we are all pretty much on the same page.