For the songs with the same exact name (i.e. Chị Tôi), the current version of TKaraoke will pick the most popular song and use its lyric. Popular here is defined by the number of views the song gets on the live database. The number of view is shown under "Thông tin về bài hát" icon on the
lyric site.
In the near future, TKaraoke will use other info in addition to the song name to pick the lyric. For example, it will use the songwriter name as well when there are more than one song in the database match the given song name. In the "Chị Tôi" case, if the songwriter is "Trần Tiến", it will use "Nhà tôi trên bến sông..." and if the songwriter is "Trọng Đài", it will use "Thế là chị ơi rụng bông hoa gạo..."
Just a heads up, in the next version, if the songwriter doesn't match, TKaraoke will not supply the lyric. If the songwriter is unknown, TKaraoke will use the current method (use the most popular song). Therefore, it's better to not supply the songwriter name than to supply the wrong songwriter name!
The next version will also has an option to populate the songwriter names for your songs automatically base on the info on the live database. This is useful for unique song names. TKaraoke will give you the songwriter names automatically based on the info on the live database. This database should be more accurate than your own listing.