[jdrnd]

I think, as a few people have commented, you are bending the strings (ever so slightly) instead of pressing straight down.
When I bought my Hamer electric, I hadn't played an electric for a number of years.
I kept complaining on the Hamer fan club forum that my guitar was out of tune. I insisted it was the guitar and not me.
They were mad at me because they felt I was dissing Hamer guitars. I dug out my old Fender Mustang and found that that guitar also did not play in tune.

After a while I got better, and the Hamer and Fender guitars played in tune (they were never out of tune).