Current and Reference Voltage to Sensors

After you have the correct voltage at a certain point, does the current that a DMM would measure at that point have to equal the current that a sensor uses? for example, a sensor i'm using needs 2.5V and says it draws something around 1mA. when i measure with my DMM it says 2.5V and about 0.4A. does this mean that it would overload the sensor if i hooked it up or would it more or less adjust the amount of current it's drawing to 1mA?also, do you guys usually use voltage reference chips to maintain a steady reference voltage? or do you just accept whatever errors a voltage divider may create?thanks.

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