The tab component () doesn't show the attribute aria-controls. This also happens on the documentation page (https://bootstrap-vue.js.org/docs/components/tabs/) which makes me think it is a bug.
To me it looks like a problem with line 617 in bootstrap-vue/src/components/tabs/tabs.js:

controls: this.tab && this.tab.safeId ? this.tab.safeId() : null,

where this.tab and this.tab.safeId are undefined - changing code to:

tab && tab.safeId ? tab.safeId() : null,

is working, the attribute aria-controls is shown in the link in the tab.

• BootstrapVue: 2.xx