Here is my understanding of your problem:
When you play the MIDI file you attached in a particular MIDI player, the notes in the second track begin to go out of sync with the notes in the first track. As part of trying to understand what is causing the problem, you want to understand how to manually convert a position in absolute ticks to a position in absolute seconds.
How to convert ticks to seconds
As Clemens Ladisch said, you should first convert delta ticks into absolute ticks. In other words, instead of using the tick position from the previous event in the track (delta ticks), calculate the tick position from the beginning (absolute ticks). You do this by adding all the delta ticks in the particular track you are concerned about up to and including the delta ticks for the event you are concerned about.
Next, to convert the amount of ticks into an amount of quarter notes, use the "ticks per quarter note" resolution specified in the MIDI file. In the MIDI file you attached, the resolution is 480 ticks per quarter note. So divide the amount of ticks by 480 to get the amount of quarter notes.
Next, as you know, each tempo event in a MIDI file is actually a conversion factor in microseconds per quarter note.
To convert an amount of quarter notes into an amount of microseconds....
First let's start with an example where there is only one tempo for the entire file:
x is the amount of quarter notes from the beginning
y is the amount of microseconds from the beginning
m is the conversion factor in microseconds per quarter note
y = m x
Now let's look at an example where there are multiple tempos in the file:
x is amount of quarter notes from the beginning
y is amount of microseconds from the beginning
m0 is the conversion factor in microseconds per quarter note from the beginning to x=a
ma is the conversion factor in microseconds per quarter note from x=a to x=b
mb is the conversion factor in microseconds per quarter note from x=b to x=c
mc is the conversion factor in microseconds per quarter note from x=c to the end
if x is between 0 and a: | y = m0 x |
if x is between a and b: | y = m0 a + ma (x - a) |
if x is between b and c: | y = m0 a + ma (b - a) + mb (x - b) |
if x is between c and the end: | y = m0 a + ma (b - a) + mb (c - b) + mc (x - c) |