Is "since I'm" now an acceptable alternative to "since I was"?
Solution 1:
Dr. Google to the rescue; looks like they didn't make it up. About half the results include that usage. (The other half has the normal usage: since meaning because.)
However, that usage is, at best, slang. As yet it is not grammatically acceptable.
Solution 2:
It's not exactly a mistake on the part of the scriptwriters. They're just reproducing the poor grammar of their characters (who may be fictional, but feasibly could exist and speak like that).
Unquestionably in my opinion the usage is ungrammatical, but that certainly doesn't mean no-one ever says it. Possibly it's related to since I's, which is "non-standard", but at least could be considered correct in terms of verb tense (the 's could stand for was, which is perfectly okay).
Solution 3:
If we change the crude example to something like, "I have been giving provocative and insightful lectures since I'm 12," the grammar would still be judged to be incorrect by the vast majority of native speakers (I think). I have heard that particular construction in two places -- in ESL classrooms, and in populations that typically speak regionally-based dialects of non-standard English.
I doubt it is a general trend. Were the characters non-native speakers? Or speaking in a strong dialect?