For styling each directional arrows(left, right,top and bottom), we have to select each arrow using CSS attribute selector and then style them individually.
Trick: Top arrow must have border color only on top side and transparent on other 3 sides. Other directional arrows also need to be styled this way.
click here for Working Jsfiddle Link
Here is the simple CSS,
.tooltip-inner { background-color:#8447cf;}
[data-placement="top"] + .tooltip > .tooltip-arrow { border-top-color: #8447cf;}
[data-placement="right"] + .tooltip > .tooltip-arrow { border-right-color: #8447cf;}
[data-placement="bottom"] + .tooltip > .tooltip-arrow {border-bottom-color: #8447cf;}
[data-placement="left"] + .tooltip > .tooltip-arrow {border-left-color: #8447cf; }