You may read my analysis of Greek J2b2-L283
here and
here, which was written before we had the Mycenaean ancient DNA. My analysis pointing that J2b2-L283 is unlikely to be present among Mycenaeans, and is as a result of later migrations from further North (Dorians, Illyrians, and later Vlachs and Albanians), seems to stand.
Regarding J2b1-M205, as Dema pointed out, in the mainland Balkans (outside of the the Mediterranean), all of it seems to fall under J2b1-M205>PH4306>Y22066 and has a TMRCA of only ca. 900-1200 years, which suggests it was likely not present there before the common era, hence the reason why (Gheg) Albanians are almost completely lacking it. Unfortunately, many people don't understand haplogroup J2b quite well, so they assume they are part of the same migration. True, J2b1-M205 has a TMRCA of ca. 6000 years, but in ancient DNA is consistently being found in the Levant area. So far the only J2b that has "deep roots" (high TMRCA) in Europe, and found in ancient DNA from the Bronze Age (Croatia) is J2b2-L283.