No, rail construction started from Madras only. By 1862, there was a continuous rail line from Madras to Beypore (Near Calicut). Construction for the line to Bangalore started from Jolarpettai in 1861-62 and was completed in August, 1864 and Bangalore Cantonment (BNC) was the original railway station in the city (SBC was constructed almost 25 years later).
In those days, most mainline routes had just a single end-to-end mail train and several passengers. The mail train would carry through coaches (what we now call slip coaches) to important destinations on the route. Traffic and population weren't so high then, so dedicated trains were not necessary for all destinations.
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So, there was one mail train that used to run between Madras and Beypore (Calicut) and it had through coaches to Bangalore (for Mysore) and to Mettupalayam (for Ooty).

Madras to Jolarpettai was completed by 1862 only. (Jolarpettai is JTJ, which is on the MAS-CBE route).
Like I said, initially there was a mail train on Madras-Jolarpettai-Calicut route, which had slip coaches to Bangalore. This is the present day 12601/02 MAS-MAQ mail. The slip coaches were detached at JTJ and proceeded to BNC. In 1908, this slip coach service was de-linked and started running as a separate train, which is the present day MAS-SBC mail.
Delhi was not an important place then....
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Delhi only became important in 1911 after it became the capital. Till then only Madras, Calcutta and Bombay were the important cities in the country.
More Indians used the trains than Britishers. The British constructed many of the lines for famine relief (to move food and supplies faster during famines). The entire MAS-GTL-RC line and many branch lines in Rayalaseema area were constructed for famine relief.