Just because a transformer coupled tube amplifier has outputs marked 4, 8, or 16 ohms doesn't mean the output impedance is actually 4, 8, or 16 ohms. The reason the bass may be tighter on the 4 ohm tap is simply because output impedance is significantly lower on that tap than the 8 ohm. Low output impedance is the reason many like solid state (voltage source, not current source) amplifiers. They have very low output impedance, typically less than .5 ohms, and many as low as .001 ohms. That low output impedance can be good if woofers aren't being controlled well by an amplifier with high output impedance resulting in woolly bass. However, if speakers have high impedance, putting a low output impedance amp on them (or using the 4 ohm tap) may over damp the woofers and give the speakers a leaner sound.
I have a small PP el84 amp that has 4, 8, and 16 ohm taps whose actual output impedance measurements are 5.6 ohms, 11 ohms, and about 20 ohms respectively. Those numbers (4,8,16 ohms) are a guideline. Also, there is always an assumption with smaller SET and PP transformer coupled amps that you aren't going to put them on speakers with extremely difficult loads that could stress them. Your Klipsch speakers are not a difficult load.