In Finland ae and oe are both typically pronounced as /e:/ when they belong to the same syllable. In (and near) Turku the pronunciations are /ai/ and /oi/. (This excludes, for example, aer and poema; this difference only concerns the diphthong.) Otherwise these pronunciations seem to coincide.
When and how did this difference appear between Turku and the rest of Finland? My understanding is that Finnish pronunciation is fairly close to classical, with Turku using a slightly older version. I am not very well familiar with the details of how Latin came to Finland, but I hope understanding this difference will shed a little more light on it.
(The question in the title also makes sense for the Finnish language, but my interest here is in Latin.)