This is not likely to be normal behavior from the D7200 or the Yongnuo trigger itself. A one-second delay usually points to a camera setting that intentionally delays shutter release/flash timing.

Check these on the D7200:

• red-eye reduction flash mode: this adds a pre-flash/light delay before the exposure
• self-timer: adds a countdown before firing
• exposure delay mode (Custom Setting d4): intentionally delays the shutter after you press the button
• remote release delay options if using an ML-L3 remote
• rear-curtain sync: if your shutter speed is around 1 second, the flash fires at the end of the exposure, which feels like a delay

A good test is to see whether the shutter itself is delayed, or only the flash pop. If both are delayed, it’s almost certainly one of the camera settings above. Since your D7100 works instantly with the same triggers, the D7200’s settings are the first thing to check.