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I had to implement the code in conditional-logic.js in order to have the functionality work well on fields which were already set before doing the update in group.js

Screenshot below:

Just a small update. We managed to work around it but we made some changes to both extensions (conditional logic and group). I know this is not ideal and on the next update we will be loosing all changes. Therefore I am attaching the code here such that the plugin author can include these changes in the next update:

meta-box-group/group.js : line 37

group.toggle.updateState = function( $group, state ) {
    var $input = $group.find( '.rwmb-group-state' ).last().find( 'input' );
    if ( state ) {
        $input.val( state );
    } else {
        state = $input.val();
    }

    // Store current state. Will be preserved when cloning.
    $input.attr( 'data-current', state );
    $input.trigger('change'); //<<--added this line so that conditional-logic will run the logic when _state changes

    $group.toggleClass( 'rwmb-group-collapsed', 'collapsed' === state )
          .find( '.rwmb-group-toggle-handle' ).first().attr( 'aria-expanded', 'collapsed' !== state );
};

meta-box-conditional-logic/js/conditional-logic.js : line 381

function guessSelector(fieldName, selectorCache) {
    if (compare(fieldName, '(', 'contains')) {
        return '';
    }
    if (!selectorCache) {
        selectorCache = globalSelectorCache;
    }

    if (isUserDefinedSelector(fieldName)) {
        return fieldName;
    }

    //Added below line to check if scope is cloneable or not
    var cloneable = $(selectorCache.$scope).hasClass('rwmb-clone');

    var selectors = [
        fieldName,
        '#' + fieldName,
        '[name="' + fieldName + '"]',
        '[name^="' + fieldName + '"]',
        '[name*="' + fieldName + '"]'
    ];

    //Added below condition to prepend the exact name attribute to the selectors array
    if (cloneable) {
        $.each(selectors, function (index, pattern) {
            var tempSelector = selectorCache.get(pattern);
            if (tempSelector.length > 0) {
                selectors.unshift('[name="' + tempSelector.attr('name') + '"]');
            }
        });
    }

    var selector = _.find(selectors, function (pattern) {
        return selectorCache.get(pattern).length > 0;
    });

    return selector ? selector : '';
}

meta-box-conditional-logic/js/conditional-logic.js : line 529

// Listening eventSource apply conditional logic when eventSource is change.
if (watchedElements.length > 1) {
    //Added the following loop, to run the coniditional logic on initialization
    $.each(watchedElements.split(','), function(){
        var $scope = getFieldScope($(this));
        runConditionalLogic($scope);
    });
    $document.on('change keyup', watchedElements, function () {
        var $scope = getFieldScope($(this));
        runConditionalLogic($scope);
    });
}