Not knowing enough details and with limited information it is very confusing.
However, from your description of the issue it appears your method and/or settings for the transformer testing is flawed.
If I understand you correctly:
Energizing the primary side of the transformer does not result in a trip condition but energizing the secondary side results in a "ground/earth fault" trip initiation.
You do not clarify but it appears you are inducing test voltage on the secondary side with the primary side "open" and disconnected (de-energized). (Are you using test equipment to do this or are you back-feeding the transformer from another source?)
Your question appears to be: Whether to alter the "ground/earth fault" pickup magnitude setting or the time duration setting on the secondary side of the transformer or at the station where the primary power is being provided from.
My questions are:
Where is the relay trip function occurring? At the primary supply source (station) or in the transformer secondary protection relaying circuit? (Location of the trip event dictates where to look for and address the cause.)
Have you tried to energize the transformer "unloaded" and disconnected from all cables and busses other than the "Y" earth/ground connection?
1. The cable/wiring and buss present/exhibit charging load during energization.
2. Where you induce the test voltage physically on the buss can and will affect results of the test due to the direction of current flow induced though the earth/ground CT. (Test lead connections and/or source attachment.)
In any case:
I would suggest:
1. You first examine the physical location of the ground buss CT and make sure it is correctly positioned and properly polarized on the buss.
2. Meggar the secondary windings in referrence to the "Y" connection and verify your system impedance is balanced.
3. Make sure the "Y" connection and earth/ground connection is properly torqued and verify the impedance "Y" to earth/ground is less then 1 ohm impedance. (If the "Y" connection and/or earth/ground is not at very low impedance, the "B" phase voltage will become unstable as well as too high in magnitude which in turn will cause false relay tripping due to the unbalance and "wild leg" induced condition.
4. If checking all of these items does not reveal the cause of the issue, I would suggest you review and verify the testing method(s) as well as the relay settings especially on the GF time and magnitude parameters.