Two issues here. Whether vermicompost can carry diseases, and whether you need to make compost tea at all.

To the first question, there are no guarantees in life, but vermicomposting is an excellent way to suppress the spread of plant diseases (I assume you mean those and not human diseases). The worms carry microorganisms with them that actively outcompete and destroy a lot of plant disease organisms. If you do have a large quantity of diseased plant material, though, you should throw it away or burn it - not compost it by any means - just to be on the safe side. But random occurrences of plant disease spread are really not a big concern with vermicomposting, if the material has had the chance to be processed thoroughly by the worms.

As to "compost tea", it's really not a beneficial practice and is a big waste of time and effort in my opinion and in the opinion of many evidence-based gardeners. I don't think it's actively harmful, but it's such an unnecessary bunch of magical thinking. Vermicompost has a lot of excellent qualities, and those qualities are not improved by watering the stuff down. Just put it onto, or into, the soil and stand back.

The most I'll ever do is throw some vermicompost in a bucket, fill the bucket with water, mix it around thoroughly and immediately pour the water on the soil - in some situations where I want the nutrients to get to the plant roots a tiny bit faster. I don't think even that's really necessary, but sometimes it's convenient to do it that way on an already planted area when there's not much rain in the immediate forecast.