  The spin orientations of spinning binary black hole (BBH) mergers detected by
ground-based gravitational wave detectors such as LIGO and Virgo can provide
important clues about the formation of such binaries. However, these spin
tilts, i.e., the angles between the spin vector of each black hole and the
binary's orbital angular momentum vector, can change due to precessional
effects as the black holes evolve from a large separation to their merger. The
tilts inferred at a frequency in the sensitive band of the detectors by
comparing the signal with theoretical waveforms can thus be significantly
different from the tilts when the binary originally formed. These tilts at the
binary's formation are well approximated in many scenarios by evolving the BBH
backwards in time to a formally infinite separation. Using the tilts at
infinite separation also places all binaries on an equal footing in analyzing
their population properties. In this paper, we perform parameter estimation for
simulated BBHs and investigate the differences between the tilts one infers
directly close to merger and those obtained by evolving back to infinite
separation. We select simulated observations such that their configurations
show particularly large differences in their orientations close to merger and
at infinity. While these differences may be buried in the statistical noise for
current detections, we show that in future plus-era (A$+$ and Virgo$+$)
detectors, they can be easily distinguished in some cases. We also consider the
tilts at infinity for BBHs in various spin morphologies and at the endpoint of
the up-down instability. In particular, we find that we are able to easily
identify the up-down instability cases as such from the tilts at infinity.
