You need to add a shell script action to your automator script, and do the actual setting in the shell script. I don't believe its possible to obtain the start time of the automator script, so you'll have to settle with a time stamp relative to the time when the shell script is executed. If you really need the start time, you'll have to add an action to record it yourself as the first step in the automator script.
In the shell, time computation is done with date.
date -v 1M
gives you the time one minute ago. If you really need it formatted in the specific way that you give above, you need to format it yourself, like so
date -v -1M '+%b %d, %Y, %H:%M:%S %p'
Here, %b, %d etc are place holders for the various timestamp components; see the man page for strftime.
Next, you need to know how to change a plist file. You can use plutil for that, like so
plutil -replace SULastCheckTime -string newvalue foo.plist
Putting it all together, the shell script could read
time=`date -v -1M '+%b %d, %Y, %H:%M:%S %p'`
plutil -replace SULastCheckTime -string "$time" foo.plist
Here, the backticks take the output of date and put it in a variable time; plutil then puts it in a file.
If you are going to use shell scripts anyway, you may consider dropping automator altogether in favor of shell scripts.