In this particular context, either are acceptable. "Out" in the context of publishing can mean "released", so it refers to a specific point in time rather than a limited period.
In other contexts, saying something "is out" at a particular time can mean for a limited period. For example, if a person said "I'm out on Saturday", that would mean they are not home that day, but it could mean they are back home the following day. By contrast, when a record or a book "comes out", it is released to the public and is then continuously available from then on.
You could say any of the following:
- The record is released in June
- The record is out in June
- The record will be released in June
- The record will be out in June
- The record will be available in/from June
- The record will be available in/from June
The tense is fine, because there is a fixed date for the record release. You can say something "is coming" when it is in the process of coming and you are anticipating its arrival, for example "my brother is coming to visit in June".