You could take a look into the following example angular/material2 Tooltip Demo
Basically you could set up the tooltip as follows (you could define not only the css but also the position, the hide delay, the show delay and if it is disable or not):
<button #tooltip="mdTooltip"
md-raised-button
color="primary"
[mdTooltip]="message"
[mdTooltipPosition]="position"
[mdTooltipDisabled]="disabled"
[mdTooltipShowDelay]="showDelay"
[mdTooltipHideDelay]="hideDelay"
[mdTooltipClass]="{'red-tooltip': showExtraClass}">
In your component then
position: TooltipPosition = 'below';
message: string = 'Here is the tooltip';
disabled = false;
showDelay = 0;
hideDelay = 1000;
showExtraClass = true;
And the css as example:
/deep/ .red-tooltip {
background-color: rgb(255, 128, 128);
color: black;
}