Block tab type is not using block config settings

We're using a custom block plugin to display an embedded Twitter timeline. I've been trying to figure out why the block works when placed in the block manager, but not when placed inside a QuickTabs block tab. Dumping the block plugin's configuration shows that when rendered inside QuickTabs, the block's config is not being used. Example of $this->configuration...

Placed by block manager and rendered on a page:

'id' => string(29) "custom_blocks_twitter_timeline"
'label' => string(0) "Foo's Twitter Feed"
'provider' => string(12) "custom_blocks"
'label_display' => string(7) "visible"
'link_url' => string(20) "https://twitter.com/Foo"
'link_text' => string(6) "Tweets"
'widget_id' => NULL
'height' => string(3) "500"
'width' => string(4) "auto"
'limit' => NULL
'replies' => boolFALSE
'theme' => boolFALSE
'chrome' => NULL
→'link_color' => string(7) "#999999"
'border_color' => string(7) "#333333"
'aria' => string(6) "polite"
'do_not_track' => boolTRUE

These match the values saved in the block config. When viewed in QuickTabs:

'id' => string(29) "custom_blocks_twitter_timeline"
'label' => string(0) ""
'provider' => string(12) "custom_blocks"
'label_display' => string(7) "visible"
'link_url' => string(20) "https://twitter.com/"
'link_text' => string(6) "Tweets"
'widget_id' => NULL
'height' => string(3) "300"
'width' => string(4) "auto"
'limit' => NULL
'replies' => boolFALSE
'theme' => boolFALSE
'chrome' => NULL
→'link_color' => string(7) "#2b7bb9"
'border_color' => NULL
'aria' => string(6) "polite"
'do_not_track' => boolFALSE

These are the default values defined in the block plugin.

When configuring the quick tab, the configuration for the block of a block tab type never displays to be able to set the block configuration.