This answer is a more detailed version of my two comments on the question.
I do not know the origin of the notation エンターティナー, but let me give a few plausible origins.
First, I think that hypercorrection is a pretty plausible reason. For example, what was written as フイルム is now also written as フィルム, reflecting the pronunciation of the original word in English better (or at least intending to do so). If one does not know the pronunciation of “entertainer” in English, one may well think that what is written as エンターテイナー is probably more precisely written as エンターティナー, “analogously” to other words such as フィルム.
A cursory look at some of the search results for ["エンターティナー" 発音] on Google seems to give enough evidence that some people indeed pronounce “エンターティナー” with the ティ /ti/ sound.
Non-standard use of letter ぃ
Second, some people seem to use little ぃ in a non-standard way; namely, to denote a weak い sound instead of modifying the preceding vowel to /i/. For example, there is a cake product called かすてぃら. If I am not mistaken, this product name is pronounced as かすていら with /i/ sound or かすてーら with long /e/ sound, never with /ti/ sound. As an another example, some people write “へい” in the Edo dialect as “へぃ”: searching ["へぃお待ち"] on Google shows 213 results (by checking until the last search-result page). For those who employ this non-standard convention, エンターティナー is pronounced as エンターテイナー with weak イ, which reflects the pronunciation of the English word as well as (or possibly even better than) the usual notation エンターテイナー.