It's a bunch of xenophobic nonsense - however it was a big driver behind the original Brexit vote. Once the UK leaves the EU (which, as set out by #30, is much further down the line), there will be no more free movement for EU citizens into the UK. In practice, very little will change.
EU citizens currently living in the UK will be able to obtain permanent leave to remain (in essence lifelong residency) as previously. Many if not most who have built their lives here will in due course naturalise (I will be doing the same). In other words, no-one will be "kicked out".
Post-Brexit, it will be very easy for EU workers to obtain working visas for the UK. First, the UK economy will remain as highly reliant on EU migrant workers as it currently is (although arguably there will be a contraction in demand as the UK economy contracts post-Brexit, as is currently forecasted). The uncertainty of Brexit has already had a big impact on employers in the UK and this is hardest felt by unskilled and low-skilled industries in particular. There continues to be a huge demand in the UK for seasonal workers in particular and EU migrants are best placed to fill these positions. Second, EU migrants are the highest contributing group to the UK fiscal budget. EU migrants contribute significantly more to the UK fiscal budget than people born in the UK (still net contributors) and non-EU migrants (net recipients).
Ironically, more specifically, what a lot people do not realise re today's election is that Corbyn is more of an arch-leaver than Johnson. Corbyn has personally always supported leaving the EU due to his protectionist policies, while the Tories have always espoused the benefits of immigration (albeit in policy but not in rhetoric).