Yes it should have been made clear to the electorate but it wasn't, like everything else and they've voted in the expectancy that immigration will drastically fall, and as you say the likelihood is that immigration will actually increase because of Brexit and emigration will fall and those who have emigrated may return because their pension is becoming worthless.
The EU classified immigrants would then join the non-EU immigrants to become a new classification of non-UK immigrants, but the Uk plans on continuing to accept immigrants from outside the EU but refuse entry to those from inside the EU
As you may note with the initial approach to India, they are not going to bow to the demands of the UK. As for China , you may have noticed that a lot of products already have "Made in China" on them. Doubtful many products in China have "Made in Britain" on them. They do not need to bow down to the Uk's demands.
Those two countries alone make up about 40% of the world, add the USA with TTIP, Canada with a 7 year long discussion for a country with a population the size of Poland and Australia which have a grand total of 23million.
Yet the UK wish to give up around 50% of their trade because of freedom of movement which in all likelihood will be part of any deal with other countries.
When the UK leave, they will have no trade deals in place. It's like starting a new company and they'll be begging to get some deals, from a very weak point. The Uk are so proud to have the 5th largest economy , what if they become the 15th largest economy or worse.