I have enabled Deterministic Encryption for my org, encrypted field Account.Name and created new Account 'MyAccount'. So, in my classes or in Developer Console I can search this account only by full name, because, as I know, DE does't support partial search, but if I use standard search (for example in Contact detail page 'Account' field), I can find this account by 'MyA' or 'myacc'. Does anybody knows why it works?
Deterministic encryption and Search are orthogonal.
When you encrypt the search indexes it will always use probabilistic encryption and you will be able to use SOSL find and retrieve the data accordingly https://help.salesforce.com/articleView?id=security_pe_search_encryption_process.htm&type=5
Deterministic encryption is an option to allow filtering in SOQL, reports or list views against the data stored in our relational database, and there you only get exact match filtering.
I hope it helps.