I've noticed that nearly all the Tempo brand primer bulbs have leaky check valves. Generally not leaking bad enough to cause serious problems though.

Try holding the bulb vertically when squeezing it, with the line to the motor up. This lets gravity help seal the check valve.

Also, depending on the outboard, the float in the carbuerater might not be shuting off, but you'd be flooding the engine if that happens.

I was told by an Evinrude mechanic that the bulb doesn't need to be rock hard, but just firm enough to ensure that the fuel line is full and the carb bowl has fuel. Once the engine starts, the fuel pump draws the fuel through the line.