The expression "tall poppy syndrome" is more to do with staying humble, as Hive account@mattclarke suggested below.

"Don't be fooled by the rocks that I got
I'm still, I'm still Jenny from the block
Used to have a little, now I have a lot
No matter where I go, I know where I came from (from the Bronx!)"

We have an expression:

"Pull your head in" and the mental image is one of a turtle doing just that. We don't have a problem with people being successful, just don't showboat about it. Or look down your nose at other people on your way up.

The biggest offender of this little rule was a tennis player by the name of Leyton Hewitt.