How to mount load-bearing assembly meant to be installed into joists
This shouldn't be a big ordeal - just get a 2x6 and cut it so that it spans at least 2 joists when oriented in the direction you want the pullup bar (perpendicular).  Use lag bolts to secure the 2x6 to the joists, then use more lag bolts to secure the pullup bar to your 2x6.

If that seems to have too much flex for you (I doubt it), you can always double up the 2x6's and use longer lag bolts to attach them to the ceiling.

Oh, also, 2x4s might work fine, but the mounting holes for your bar seemed too wide for that.