Counting same contact per row when mixed in with multiple contacts

mouzicanat1  for whatever reason you can't do what AlexisOlson  is suggesting, DAX can still rescue.

You need a slicer table first

Slicer =
VAR _1 =
    ADDCOLUMNS ( tbl, "new", SUBSTITUTE ( tbl[Contacts], ",", "|" ) )
VAR _2 =
    GENERATE (
        _1,
        ADDCOLUMNS (
            GENERATESERIES ( 1, PATHLENGTH ( [new] ) ),
            "persons", TRIM ( PATHITEM ( [new], [Value], TEXT ) )
        )
    )
RETURN
    SUMMARIZE ( _2, [persons] )

which will give you this

then you can write a measure like this

Measure =
VAR _1 =
    ADDCOLUMNS ( tbl, "new", SUBSTITUTE ( tbl[Contacts], ",", "|" ) )
VAR _2 =
    GENERATE (
        _1,
        ADDCOLUMNS (
            GENERATESERIES ( 1, PATHLENGTH ( [new] ) ),
            "persons", TRIM ( PATHITEM ( [new], [Value], TEXT ) )
        )
    )
VAR _3 =
    COUNTX (
        FILTER ( _2, [persons] = SELECTEDVALUE ( Slicer[persons] ) ),
        [persons]
    )
RETURN
    _3

If you want the Total to be reconciled too

Measure2 =
VAR _1 =
    ADDCOLUMNS ( tbl, "new", SUBSTITUTE ( tbl[Contacts], ",", "|" ) )
VAR _2 =
    GENERATE (
        _1,
        ADDCOLUMNS (
            GENERATESERIES ( 1, PATHLENGTH ( [new] ) ),
            "persons2", TRIM ( PATHITEM ( [new], [Value], TEXT ) )
        )
    )
VAR _3 =
    SUMX (
        ADDCOLUMNS (
            Slicer,
            "ct", COUNTX ( FILTER ( _2, [persons2] = EARLIER ( [persons] ) ), [persons2] )
        ),
        [ct]
    )
RETURN
    _3

pbix is attached