June 1st is a pretty big date on the NFL calendar. Even though it has no official title, the first of June signifies a shift in how traded or released players contracts are weighed against the salary cap. Pro Football Network probably breaks it down best:
“If a player is released or traded after June 1, no further prorated money accelerates onto the cap. Instead, that money accelerates onto the following year’s cap.”
Long story short, (most) players are cheaper to release after June 1st and if you trade for player they will cost you less as well.