  We present Chandra X-ray observations of four optically-selected tidal
disruption events (TDEs) obtained 4-9 years after discovery. Three sources were
detected with luminosities between 9X10^40 and 3X10^42 erg/s. The spectrum of
PTF09axc is consistent with a power law of index 2.5+-0.1, whereas the spectrum
of PTF09ge is very soft. The power law spectrum of PTF09axc and prior
literature findings, provide evidence that TDEs transition from an early-time
soft state to a late-time hard state many years after disruption. We propose
that the time to peak luminosity for optical and X-ray emission may differ
substantially in TDEs, with X-rays being produced or becoming observable later.
This delay helps explain the differences in observed properties such as
L_opt/L_ X of optically and X-ray selected TDEs. We update TDE rate predictions
for the eROSITA instrument: it ranges from 3 per yr to 990 per yr, depending
sensitively on the distribution of black hole spins and the time delay between
disruption and peak X-ray brightness. We further predict an asymmetry in the
number of retrograde and prograde disks in samples of optically and X-ray
selected TDEs. The details of the observational biases can contribute to
observed differences between optically and X-ray selected TDEs (with optically
selected TDEs being fainter in X-rays for retrograde TDE disks).
