The railway & engineering connection is very interesting. Benjamin Willoughby Tyers was a steam engine maker/fitter by trade, presumably employed at the GWR works in Swindon. I guess that he was seconded to the East Indies and India for a period (or two?) for sometime between 1853 and 1876. The family does not appear in the 1871 census in Swindon. However, the only son I know of (John Emanuel Tyers) was a mining engineer at Rewah (not far from Allahabad), not a railway man. It would appear that these Tyers (father or son) were not in India between 1876 and 1881.The birthdate of your Henrietta makes it unlikely that she was part of this family, but a cousin perhaps?
John's details: John Emanuel Tyers b.1853 Swindon. m.26.2.1881 Emma Leah (17) d/o Wm King, St Marks, Swindon. (Emma Lea d/o Wm, coal dealer, & Emma Lea King, bapt.2.5.1864 St Marks). 1881census: 555 Collyhurst Rd, Manchester, age 27, mining coal engineer and Emma, in the house of Thomas Tyers 52 ale & porter merchant (uncle) and his family. My grandmother’s address book (±1913): JE Tyers, Rewah State Collieries, Umaria, Central India. Birth notices from the Swindon Advertiser: April 28 at Mohpani, C.P., the wife of J.E. Tyers, A.M.I.M.E., of a son (26.5.1888); February 20 at Mohpani, C.P., India, the wife of J.E. Tyers, A.M.I.M.E., of a son (22.3.1890). There may well have been other children - I have not checked every issue of the paper!! There may also be a connection with Hyderabad Volunteer Rifles around 1899, but I have lost the link and details. Doh!