We cruised Alaska (different cruise line) during the second week of June.
The weather was cool to cold (highs in the 40s on 2 port days in the high 50s the other 2). We are from Texas where the temperatures were already in the high 90s so it was cold to us. We were told this was cooler than usual. We only had rain one day (Juneau).
If you want to see the salmon run, you will have to cruise in July. The salmon run also brings out the other wild life. We didn't see bear or moose. The tour guides told us it was too early. We did get to see tons of bald eagles which was amazing.
The only thing I would add is that no matter when you go, if you can, get a veranda room. It is worth it for the views. It was also nice on the day we sailed the Tracy Arm to stand on our own balcony and then duck back into the room when it got too cold. With the air coming down off the glacier, the wind chill was 31 that day. We also got hot chocolate and pastries in the morning and ordered room service for lunch. We did go up top when we got all the way in to the arm for a 360 view, but as cruising the arm takes all day, it was nice to have our own retreat where we could still enjoy the view.