Why the job's next_run_time is wrong?
The docs on sysjobschedules reveal that the data inside refreshes every 20 minutes.


  NOTE: The sysjobschedules table refreshes every 20 minutes, which may
  affect the values returned by the sp_help_jobschedule stored
  procedure.


Which is why your next_run_date &amp; next_run_time columns could show out of date data.

For a much longer answer &amp; deep dive. Check out this answer by Aaron Bertrand 

He talks about using dbo.sysjobactivity. 

You could use the next_scheduled_run_date, which is a datetime column from this dmv.

Example query:

SELECT sj.Name, 
next_scheduled_run_date
FROM msdb.dbo.sysjobs sj
JOIN msdb.dbo.sysjobactivity sja
ON sj.job_id = sja.job_id
WHERE session_id = (
    SELECT MAX(session_id) FROM msdb.dbo.sysjobactivity); 


With the max(session) used because the agent starts a new session each time it restarts.

This results in

Name                            next_scheduled_run_date
LSAlert_My_machine              2019-10-20 11:34:00.000
LSRestore_My_machine_Test42     2019-10-20 11:45:00.000
LSCopy_My_machine_Test42        2019-10-20 11:45:00.000
syspolicy_purge_history         2019-10-21 02:00:00.000




SSMS

When tracing what SSMS is doing to get the job info when calling job activity monitor. the last_run_date &amp; last_run_time are taken from the xp_sqlagent_enum_jobs procedure, in a cursor wise manner.

You could get the job info &amp; place a cursor over it by using this procedure.

An example of getting the info for one job:

DECLARE @job_id uniqueidentifier
DECLARE @job_owner varchar(255)
SELECT @job_owner = SUSER_SNAME()

SELECT @job_id=job_id FROM msdb..sysjobs 
WHERE name = 'LSAlert_My_machine'
    EXECUTE master.dbo.xp_sqlagent_enum_jobs 1, @job_owner, @job_id;


2nd until 5th columns returned by the procedure:

Last Run Date   Last Run Time   Next Run Date   Next Run Time
20191020        114400          20191020        114600


If you wish to run the procedure for all jobs:

DECLARE @job_id uniqueidentifier, @job_name varchar(255)
DECLARE @job_owner varchar(255)
SELECT @job_owner = SUSER_SNAME()
DECLARE @xp_results TABLE(Job_name varchar(255),Job_Id varbinary(16),last_run_date varchar(10),last_run_time varchar(10),next_run_date varchar(10), next_run_time varchar(10), next_run_schedule_id int, requested_to_run bit,request_source int, request_source_id int, running bit, current_step int, current_retry_attempt int, [State] int)

DECLARE C CURSOR FAST_FORWARD READ_ONLY FOR 
SELECT [name],job_id FROM msdb..sysjobs 
OPEN C
FETCH NEXT FROM C INTO @job_name,@job_id
WHILE @@FETCH_STATUS = 0
BEGIN

INSERT INTO @xp_results(Job_Id,last_run_date ,last_run_time ,next_run_date , next_run_time , next_run_schedule_id , requested_to_run ,request_source , request_source_id , running , current_step , current_retry_attempt , [State] )
    EXECUTE master.dbo.xp_sqlagent_enum_jobs 1, @job_owner, @job_id;

UPDATE @xp_results
SET Job_name = @job_name
WHERE Job_Id = @job_id;

FETCH NEXT FROM C INTO @job_name,@job_id
END
CLOSE C
DEALLOCATE C
SELECT Job_name,last_run_date,last_run_time,next_run_date,next_run_time 
FROM @xp_results;


Example output

Job_name                        last_run_date   last_run_time   next_run_date   next_run_time
LSAlert_My_machine              20191020        115800          20191020        120000
LSCopy_My_machine_Test42        20191020        114500          20191020        120000
LSRestore_My_machine_Test42     20191020        114500          20191020        120000