I just wanted to provide a little background so the community is informed about where we are on this issue.
Why timestamping has changed
The core team made changes to Collect 1.6.1 which fixed some long-standing bugs. We did not know that form designers had built some timestamping like you've described on these bugs.
We explained our rationale for these fixes here and here and I'd encourage you to read those threads.
Potential workarounds
If you need an immediate workaround, you can try Greg's solution here, but I should caution you that we haven't tested it and can't guarantee it works or is compliant.
You can also just use an older version of ODK Collect from here.
Reliable timing is coming soon!
Reliable timing is coming to ODK very soon. It takes time because this needs to be done in a way that's compliant with the spec, tested extensively to catch all the corner cases, and rolled out across the tools in a coordinated way.
All this to say that it's coming, but it's not easy to do. You can follow and participate in the many discussions we've had over the last few months: