It depends. If we have an infrastructure project in my home state of Baden-Württemberg, then Bavaria doesn't always have to pay directly. There may be an extra grant from Federal funds, which means they pay some of the cost indirectly, but that would mean Baden-Württemberg has to apply for the grant, and then representatives of all sixteen states have to agree to it in a majority vote, as our upper house, the Bundesrat, (effectively our version of the House of Lords) is made of representatives of the states.
At the moment the decision to make crossrail or HS2 is made in London and the other nations are told they are contributing to it. That may be reasonable but then saying this is a "Scottish" or indeed Welsh or Northern Irish deficit.
I think that's one of the arguments made by the Independence movement.
Possibly, or if they are 'contributing' to infrastructure projects that benefit London, then they'd be better off independent.
I'm not saying that's a black-and-white issue or that there will be only sunlit uplands, but relying on figures generated by the British Civil Service which really support the UK government (if they don't the aren't doing their job, if you think about it) is a shaky basis as an argument for the union of the UK.