updated demo, Sql Server

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create table records (CustName   varchar(100), Country varchar(100),    RecordedTime datetime) ;
insert into records  values
('Alex','Australia','2018-Jun-01 08:00 AM')
,('Alex','China','2018-Jun-01 10:00 AM')
,('Alex','Japan','2018-Jun-01 11:00 AM')
,('John','Australia','2018-Jun-01 08:00 AM')
,('John','China','2018-Jun-02 08:00 AM')
,('Bob','Australia','2018-Jun-02 09:00 AM')
,('Bob','Brazil','2018-Jun-03 09:50 AM')
,('Bob','Africa','2018-Jun-03 11:50 AM')
,('Bob','India','2018-Jun-03 12:55 AM');

declare @d date='2018-Jun-03'

; with Indexer as 
(
    select 
        *, 
        rn= row_number() over(partition by CustName order by RecordedTime),
        rn2=row_number() over(partition by CustName order by RecordedTime desc)
    from records
)
,GetValidCustomerRecords as
(
    select 
        CustName,
        Country,
        RecordedTime,
        Audit   = case when cast(RecordedTime as date)=@d and rn=1 then 'add' else 'change' end,
        History = case 
                    when cast(RecordedTime as date)=@d and rn=1 
                    then 'new' 
                    when cast(RecordedTime as date)<@d and rn=1 
                    then 'before'
                    else 'current' end
    from Indexer i 
    where CustName in
    (
    select 
        distinct CustName 
    from records
    where cast(RecordedTime as date)=@d
    ) 
    and (rn=1 or rn2=1) and cast(RecordedTime as date)<=@d
)

select * from GetValidCustomerRecords
order by CustName, RecordedTime

View schema
Execution time: 0,02 sec, rows selected: 3, rows affected: 9, absolute service time: 0,17 sec