The timing is correct and it is doing what what we expect it do. See some neat coin. timing peak shift for 0.95 GeV/c and 1.37 GeV/c protons.
Here is some clarification on the variables (after getting some hints from Vince):
When looking at the coin. time, one should look at the TDC spectrum of proton trigger in RHRS (which provides stop), since electron (LHRS) starts the coin. time.
The relevant variable DBB.lt1. You can see clean window size (~150ns) and peak in the middle with no additional peaks.
Figure 1
Figure 2