To store the CPUID on which a tape has been created you need to code the TMOKEYxx to obtain the CPUID and store it in the ACCT field. You can also use TMSXITJ and TMSXITC to obtain and store the CPUID in the ACCT field. This is the only place to store the information and have it stay static during the life of the tape data set.
If you change the TMOKEY00 to have the CPUID stored or have coded the exits you must restart TMSINIT to pick up the change. If you used the exits you will also need to reload them via CAS9.