Google Trends shows that "Evictor" is a good deal more popular than "Evicter", but that is most likely due to a particular product which uses the former spelling.
I would used evictor. But I don't think this is a matter of "correctness".
As you note, the two words each have dictionary entries and certainly mean the same thing. One could dive into the etymology of -er and -or as in this question, but you didn't ask about this. I don't think you're looking for a post hoc justification of which is theoretically correct, but rather asking "which word should I use".
An easy answer is to use whichever occurs more commonly. By looking at Google Ngrams, we see that evictor is in fact significantly more common in modern usage. Note that, unlike Google Trends which reports search volume, Google Ngrams relies on occurrences in books. This often makes it a better tool to study the use of language.
Another thing to note in the Ngrams graph is that evicter was much more popular until the 19th century. This trend is also documented in the OED entry for the word. Perhaps historical popularity explains why evicter is still used from time to time, even when evictor is vastly more popular today.
I think you are using dictionaries that are responding more rapidly to changes in English use online than the standard dictionaries. I did not recognise the word(s) you are asking about, and it turns out that neither the Merriam Webster (US) English dictionary, nor the Cambridge nor the Collins (British) English dictionaries recognise the word.
There is no reason why the word should not exist, regardless of the spelling, with the obvious meaning of 'one who evicts'. [EDIT. In fact it has existed. The full Oxford English Dictionary (1992) cites it in reference to both conquerors driving out or bailiffss driving out tenants and spelled victor with victer as an alternative. But its most recent use is cited for 1888, after which it may have fallen out of use.]
It is derived from the Latin verb vinco = I win/conquer, from which can be derived the noun victor from its supine, victum. The ending of the English noun would, therefore, and of most nouns so derived, end in '-or' rather than '-er', which is the ending for English words with Teutonic endings, such as Father, maker, banker, runner.
However, in English, rules are there to be broken. I know of one exception, which is the use of the -er ending for the word adviser for UK local education authority officers, employed to guide teachers and leaders in schools. This spelling in -er is noted in Merriam, with the -er ending as an acceptable alternative.
So by all means coin this word with either spelling. Who knows? It might finally reach the major dictionaries.