Unable to find any time to get deep into this. For now I tried to edit TTSSEQ.INI only to find out that there is no 'IgnoreMIDIInTimeStamps= ' in it or any anything close to it. I juggle between two computers in both my houses. Both run Win10 64bit. Intel Core i3-4150 Haswell 3.5 GHz. One is pretty old with Intel core2duo 2.80GHz. Mostly recorded using Maudio keystation.
To make sure the midi controller is not the issue behind this I even tried recording using Sonar's Virtual controller. Used both mouse and the computer keyboard to input notes. The latency is just the same as how it is while using midi controller. So this is not related to the controller. I am sure of that now. I don't even think there is any additional issue here. As a matter of fact I have recorded for years and what I have observed is that although the notes may go till 240ticks ahead sometimes, they are just about a 120 ticks ahead(on average). Only few notes may go till 240 ticks. 120 ticks ahead is what I get normally. Not 240 ticks ahead as it is in my first screen shot. I am not sure why it is so in my first screen shot. May be while playing to a metronome and repeatedly hitting the note I might have played all the notes bit early. That is also possible or there was some other issue. Not sure though. But usually I only get only abt 120ticks ahead, so I guess we can ignore the first screen shot for now. I recorded a few notes now please go by these ones.
Both of these I rec 2 days back while making that lengthy post with synth audio screen shots.
This is the one I recorded with 100ms latency
100ms (Do notice here I have recorded some notes continuously at 240ticks ahead. So may be I am prone to making this mistake while repeatedly playing the notes.)

(open the image in new tab to see it clearly)
10ms 
This one I rec now today with 31ms latency
31ms
Just hitting the same note repeated might not be a good way to test this. I might be continuously hitting bit earlier or later. so I recorded a melody to see how it comes. 31ms latency here as well.
melody31ms
continuation

May be some more analysis is need. No time for now. Will get back 2morrow. Do interpret these. Here in the 10ms screenshot I am not sure why I got that much ticks ahead while playing with latency of 10ms. May be I am such a bad player who has the habit of playing everything bit ahead. Anyway thanks once again for all the help till now.