The problem is here
the first and second ISR addresses are true
but the second merge in first
update your code to this


ORG 000Bh
LJMP TIMER0_ISR

ORG 001Bh
LJMP TIMER1_ISR


TIMER0_ISR:
PUSH ACC
PUSH PSW
CLR TR0
MOV TH0,#HIGH RESET_VALUE2
MOV TL0,#LOW RESET_VALUE2
SETB TR0
DJNZ MTICKS,EXIT_RTC2
MOV MTICKS,#2
INC MSEC
MOV R6,MSEC
CJNE R6,#10,EXIT_RTC2
MOV MSEC,#0
INC SECOND
MOV R6,SECOND
CJNE R6,#60,EXIT_RTC2
MOV SECOND,#0
INC MINUTE
MOV R6,MINUTE
CJNE R6,#60,EXIT_RTC2
MOV MINUTE,#0
INC HOUR
EXIT_RTC2:
POP PSW
POP ACC
RETI

; Timer1 interrupt routines
TIMER1_ISR:
PUSH ACC
PUSH PSW
CLR TR1
MOV TH1,#HIGH RESET_VALUE
MOV TL1,#LOW RESET_VALUE
SETB TR1
DJNZ TICKS,EXIT_RTC
MOV TICKS,#20
INC SECONDS
MOV A,SECONDS
CJNE A,#60,EXIT_RTC
ADD A,TL1
ANL A,#00001111b
MOV password,A
MOV SECONDS,#0
INC MINUTES
MOV A,MINUTES
CJNE A,#60,EXIT_RTC
MOV MINUTES,#0
INC HOURS
EXIT_RTC:
POP PSW
POP ACC
RETI

in your code when you write [org 1bh] then
you damage to your interruot 0 service routine
because TIMER0_ISR is about 40 bytes
and the reserved space for TIMER0_ISR is only 8 bytes
so you must exit from TIMER0_ISR with LJMP at first.
I Hope It Will be useful for you!
Mehdi