Modbus: Sensors timed out when plugging another sensor
Based on your question and comments this is what I think is happening:

The RS485 transceiver you are using needs two (or at least one) control pins (DE or drive enable, which switches on the RS485 side when it is brought high and ~RE or not read enable which makes the chip accept messages from the bus when it's low). 

Those two pins are likely connected directly to digital output pins on your Arduino microcontroller. That is fine as long as the micro is operating normally but during the boot up sequence some pins have different functions or are floating (not high nor low). That is probably making the DE signal on the transceiver go up for the whole boot up time (1-3 seconds) preventing all other devices on the bus to access it (a two-wire RS485 bus is half duplex so there is only one device driving the bus at all times).

To fix your issue you might want to add pull down resistors (probably 3.3 or 4.7 k Ohm) to the DE line. If that is not successful you might want to read the particulars of the behavior of the pins you are using at boot up.

If you are wondering why the same thing is not happening when you use a different power supply, the answer is right there on your scope captures: it is actually happening but to a lower extent, low enough not to interfere with the bus.