Did you rebind? (link)
Bind each receiver at a time be sure that the other receiver is turned off.
No it is not a normal situation, could be a real issue, but you need to bind firstly.

Link Procedure
Each transmitter has an individually assigned, unique ID code. In order to start operation, the receiver must be linked with
the ID code of the transmitter with which it is being paired. Once the link is made, the ID code is stored in the receiver and no
further linking is necessary unless the receiver is to be used with another transmitter. (For T/R set, the link is already done at
factory. When you purchased another R606FS, this procedure is necessary; otherwise the receiver will not work.
1. Place the transmitter and the receiver close to each other within one (1) meter
2. Turn on the transmitter.
3. Check the LED that is placed on the back side of the transmitter to see if the RF signal is active. When the green LED is ON
solid, the RF signal is being sent.
4. Turn on the receiver.
5. Press down the "ID SET" switch for more than one second, and release the switch. The receiver starts the linking operation.
6. When the linking is complete, the LED in the receiver will change to solid green. Please confirm that the servos will now
operate by your transmitter. Please refer to the table below for the LED status of the receiver's condition.
No signal reception Red : On
Receiving signals Green: On
Receiving signals, but ID is unmatched. Green: Blink
Unrecoverable failure (EEPROM, etc.) Red and Green
turn on alternately.

*taken from Futaba 6 channel 2.4 system manual.