Ok, old versions of GNU coreutils (before 7.5) don't have an easy workaround (as far as I know), but newer versions (since 7.5) have a stdbuf command you can use to force split (or any other coreutil program) to immediately print its output. In your case, you can use:
~/coreutils/bin/stdbuf -o0 ~/coreutils/bin/split --verbose -d -u -l 10000000 1>out & tail -f out
That will run split with output buffering disabled.
Please note the -u option (unbuffered) in split does not affect the message printing, only the data it's splitting (it feels slower if you disable that buffering).
Information about stdbuf: http://www.gnu.org/software/coreutils/manual/html_node/stdbuf-invocation.html
For an alternative when using older coreutils versions, check this solution using command unbuffer from the package expect (tcl): https://unix.stackexchange.com/questions/25372/turn-off-buffering-in-pipe