comparison of two unsigned bytes strange behavior

Projects Programming
5

UKHeliBob:
My suspicion is that the calculation is being done using integers but try this

void setup()

{
 Serial.begin(115200);
 byte start = 253;
 byte mil = 253;
 byte period = 3;
 mil++; // 254
 mil++; // 255
 mil++; // 0
 mil++; // 1
 mil++; // 2
 Serial.println(mil); // prints 2
 Serial.println(mil - start); // prints -251
 if ((byte)(mil - start) >= period)
 {
   Serial.println("Time passed");
 }
}

void loop()
{
}

Works..
But if a cast is needed anyway,
A) Can I assume that for checking time elapsed with millis I should always cast the subtraction?
B) Doesn't it imply that in the "Using millis() for timing. A beginners guide" (thank you for this excellent one) a casting is missing in the examples and otherwise it actually won't handle correctly the millis overflow?