The three gems in the first video and the Hindolam Thillana in the next video are structured by Sri.TMT in his unique style. He used to be very particular about the gradual and striking improvisation of the structure of compositions and raga/thanam/kalpana swaram/neraval essays.
In my days of learning from Sri.TM Thyagarjan legendary musicians used to drop by for his guidance in structuring krithis, varnams, etc. TMT "padantharam" lies in his formidable discipline in maintaining the tempo and structure of presentation.
With TMT Sir after my learning session (90s)