Try replacing code after <?php if ($_attributeValue): ?>
, in attribute.phtml
with following:
<?php if ($_attributeValue): ?>
<?php if ($_attributeType === 'your_type'):
$objectManager = \Magento\Framework\App\ObjectManager::getInstance();
$category = $objectManager->get('Magento\Framework\Registry')->registry('current_category');
if (strtolower($category->getName()) === 'category_to_display'): ?>
<?php /* @escapeNotVerified */ echo $_attributeValue; ?> <!-- add your tab logic here -->
<?php endif; ?>
<?php else: ?>
<div class="product attribute <?php /* @escapeNotVerified */ echo $_className?>">
<?php if ($_attributeLabel != __('none')): ?><strong class="type"><?php /* @escapeNotVerified */ echo $_attributeLabel?></strong><?php endif; ?>
<div class="value" <?php /* @escapeNotVerified */ echo $_attributeAddAttribute;?>><?php /* @escapeNotVerified */ echo $_attributeValue; ?></div>
</div>
<?php endif; ?>
<?php endif; ?>
change your_type
to your declared attribute type, change category_to_display
to your desired category name (chain || to add more categories to include tab). Add your code to add your tab logic here