You're changing focus and triggering focus events ... you're also popping up popups, popups are annoying :) its better to validate on key without popups, popup at most only once on submit, on all others ring the bell and flash invalid

#!/usr/bin/perl --
use strict;
use warnings;
use Tk;

my $mw = tkinit;
my $name = $mw->Entry(  -validatecommand => \&nodigits, -validate => '
+key',)->pack;
$name->focus;
#~ $mw->WidgetDump; use Tk::WidgetDump;

$mw->MainLoop;

sub nodigits {
    my( $newstring, $difference, $oldstring, $index, $insertOrDelete )
+ = @_;
    my $entry = $Tk::event->W;
    if( $newstring =~ m/\d/ ){
        $entry->bell;
        $entry->configure( -bg => 'red' );
        $entry->after( 300, sub { $entry->configure( -bg => 'white' ) 
+} );
        return undef;
    } else {
        $entry->configure( -bg => 'white' );
        return 1;
    }
}
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