This may be the first time an answer to a question on this site was "the automatic translation got it right". However, this time the automatic translation did get it right.
偽 is a fairly common prefix that can be attached to other words to mean a fake version of that thing, although it has slightly broader applications than the English word
fake and can also mean something like
pseudo. For example, 偽医療 is the word for fake medicine while 偽中国語 is a type of Japanese internet slang that closely resembles Chinese.
While it is hard to know the exact intent of the speaker without more context,
偽ツンデレ almost certainly refers to someone who appears to be
ツンデレ but in fact is not. This could imply that the person was intentionally pretending, or not.