You are correct while Mississippi is a part of the Driver's License Compact (DLC) that requires member states to exchange information regarding traffic violations but Tennessee dropped out of the Compact in 1997. Even without being part of the DLC any longer, the TN Department of Safety has decided to report tickets back to your home state if you are cited for a traffic violation in TN with an out of state license.
The driver records section of the Mississippi Department of Public Safety (DPS) told us that if you are found guilty of a moving violation out of state they will normally receive in the conviction information from the other state and then place that offense on your Mississippi driving record. So Tennessee should inform the Mississippi DPS of the moving violation, speeding in your case, when you are convicted of the offense. Mississippi will then put the speeding infraction on your MS driving record, as you mentioned Mississippi does not have a points system.
Once the TN speeding ticket is on your record it will be treated as if it occurred in state. Potential employers as well as your insurance company can thus see the speeding violation conviction. It will depend upon your insurance company's rating system to determine if this out of state (TN) speeding ticket will affect your insurance premiums.
If your Mississippi auto insurance rates go up due to this out of state ticket you can click here to get low cost car insurance quotes.