Is the difference *EXACTLY* one hour (within a few seconds)? Definite time zone issue. Note that the definition of time zone has changed in various areas in the last few years (the US is one such area). Most likely your old 9.2 installation has an incorrect time zone definition. Time zone definitions are complex; they are stored in a directory of binary files, on my system /usr/share/zoneinfo has 476 files. You could become an expert in how time zones are defined and managed, and correct all those files, but it would be much easier to use a modern installation.
Before you do anything else, make sure you have the correct time zone set on client and server, and you are running both with correct and up-to-date timezone definitions. Without that, you'll just keep confusing yourself (and us).
You say you "changed client time zone". What do you mean by that? And then you say that the "client time sync". How did you verify that?
Question 1: You changed the server time with date command. Why did you do that? You NTP server needs to have some source for setting its clock itself. Usually, local NTP servers are themselves NTP clients, which usually synchronize to other (better) NTP servers. For example, my home machine is set up to be the NTP server for everything inside the house, but it is also a NTP client, which is configured to get the time from us.pool.ntp.org. Sometimes, NTP servers have their own source of accurate time; for example, one can now buy GPS receivers for less than $100 that are accurate to milliseconds and connect with serial (RS232) ports, and use those as a source of a pretty accurate clock. Anyway, you did step the time forward with date. That probably screwed up your NTP server. I would definitely restart it. Manually changing the server clock while a NTP server is running sounds risky, and you should probably stop doing it.
However, restarting your NTP server immediately causes a problem for the NTP client (your Cisco). Often, NTP clients are configured to only be able to drift the clock very slowly (and catching up a while hour would take too long to be practical), but they can also be configured to make a big "time jump" when they start. On FreeBSD NTP clients, you can configure that by setting the variable "ntpd_sync_on_start" to yes in /etc/rc.conf. No idea how to do that on a Cisco.