"Immigrate" is used appropriately seeing as how the sentence is about immigration to Singapore.
"Emigrate" would be used had the sentence been written along the lines of, ". . . making it easier for them to emigrate from India to Singapore."
You could just say "'migrate' from India to Singapore."
'Immigration' is used to refer to population influx into an area.
'Emigration' is used to refer to population outflux from an area.
If you are referencing the migrant, you can just say 'migrate.'
If you want to refer to the migrant in relation to a source/departure area, you use, 'emigrate,' e.g. 'an emigrant of India' or 'emigrating from India.'
If you want to refer to the migration in relation to a target/arrival area, you use 'immigrate,' e.g. 'an immigrant of Singapore,' or 'immigrating into Singapore.'
I think 'immigrant' and 'immigration' are more prominently used terminologies because of a general bias toward immigration-awareness as nativism leads people to identify and control immigration.
If the primary political interest was in preventing escapes, such as where slavery or other population-retention was a major interest, then there would be more public discourse about 'emigration' and 'emigrants,' along with 'exit-phobia' instead of xenophobia. I.e. political propaganda would be more concerned and angered with people leaving/emigrating than with people coming into an area.