Inrush current ?
https://en.wikipedia.org/wiki/Inrush_current
That's what's wrong. 1N4007 diodes are 1Amp diodes. When you switch on the power, it may take several milliseconds to fully charge your input filter caps. That time period may exceed the 1N4007's transient overload capability so they see a short-circuit and die. Inrush current at cold power-on can reach 10's of amps, depending on the cap characteristics!
Also, your 3-terminal regulators may draw up to 2+ amps when short-circuited or overloaded. The 1N4007's overload rating is for very short transients, not continuous current. So, they can overheat and short/open.
Use minimum 3Amp diodes or a modular 3+Amp FW Bridge. I build that schematic (with some modifications) all the time with no problems.
There is no problem with the capacitors, as drawn.
Also, fuse your hot input lead to your transformer (after the on/off switch not shown) for safety.