In any synchronous generator (more correctly called an alternator) regardless of the type of prime mover (steam turbine, or gas turbine, or reciprocating engine, or hydro turbine, etc.) when excitation is increased more DC current/voltage is applied to the rotating field conductors, and when excitation is decreased less DC current/voltage is applied to the rotating field conductors.
When the generator is NOT synchronized to a grid with other generators and their prime movers but is at rated speed and excitation is changed this causes the generator AC terminal voltage to change--increasing excitation causes the generator AC terminal voltage to increase, and decreasing excitation causes the generator AC terminal voltage to decrease.
When the generator IS synchronized to a grid with other generators and their prime movers and excitation is at the level that makes the generator terminal voltage exactly equal to the grid voltage the power factor <i>of the generator</i> will be 1.0, or unity. And there will be zero amperes of reactive current flowing (no leading reactive current and no lagging reactive current). Now, if excitation is increased from this point the power factor will begin to decrease from 1.0 and lagging reactive current (VArs) will begin to flow in the generator's stator (AC) windings. Continuing to increase excitation will cause the power factor to decrease further, and the amount of lagging reactive current (VArs) to continue to increase. Lagging VArs <i>from a generator's perspective</i> are generally considered to be positive VArs as they are considered to be flowing out of the generator.
If excitation is decreased from the point at which generator terminal voltage is exactly equal to the grid voltage and the generator power factor is 1.0 (unity) and there are zero VArs (reactive current amperes) the generator power factor will begin to decrease from 1.0 in the leading direction, and the reactive current amperes (VArs) will start to increase in the leading direction. Continuing to decrease the excitation even further will cause the power factor to continue to decrease in the leading direction and the leading reactive current (VArs) to continue to increase. Leading VArs are generally considered to be negative VArs as they are considered to be flowing in to the generator.
Increasing the excitation above that which makes the (AC) generator terminal voltage above that of the grid voltage <i>when the generator is synchronized to the grid</i> is called "over-exciting" the generator, or over-excitation. Over-excitation is not bad, and most AC generators are designed to run in an over-excited condition (because most grids require lagging VArs from the generator to support the grid). Excessive over-excitation can cause damage to the generator rotor (field) windings.
Decreasing the excitation below that which makes the (AC) generator terminal voltage below that of the grid voltage <i>when the generator is synchronized to the grid</i> is called "under-exciting" the generator, or under-excitation. Under-excitation is not bad, but most AC generators are not designed to be run in an under-excited condition and so generally under-excitation (leading VArs and a leading power factor) are generally to be avoided.
Now, we don't know what language your DCS displays are configured with, so it's difficult for us to say what TSI and TSE mean; perhaps you can use the above information to understand what the two terms mean. And, it's not clear why the title of this thread mentions steam turbines and the question is about (or seems to be about gas turbines). Not all power plants are the same, and some use transformer tap changers to control power factor and/or VArs between generators and/or between the plant and the grid. Hopefully you have enough information now to be able to make sense of the abbreviations on the DCS display(s) with regard to excitation.