Tax implications are not impacted by stock splits. Cost basis should automatically adjust within 3-5 business days to show the new per share amount as a result of the split.
For example, if you paid $1,000 for 10 shares and now have 40 shares as a result of the split, your total cost basis remains $1,000, but your cost basis per share has been reduced from $100 ($1,000/10 shares) to $25 ($1,000/40 shares).